{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "import sympy as sy\n",
    "sy.init_printing() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(precision=3)\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Eigenvalue and Eigenvector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An  <font face=\"gotham\" color=\"red\">eigenvector</font> of an $n \\times n$ matrix $A$ is a nonzero vector $x$ such that $Ax = \\lambda x$ for some scalar $\\lambda$. A scalar $\\lambda$ is called an  <font face=\"gotham\" color=\"red\">eigenvalue</font> of $A$ if there is a nontrivial solution $x$ of $Ax = \\lambda x$, such an $x$ is called an eigenvector corresponding to $\\lambda$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rewrite the equation,\n",
    "\n",
    "$$\n",
    "(A-\\lambda I)x = 0\n",
    "$$\n",
    "\n",
    "Since the eigenvector should be a nonzero vector, which means: \n",
    "\n",
    "1. The column or rows of $(A-\\lambda I)$ are linearly dependent\n",
    "2. $(A-\\lambda I)$ is not full rank, $Rank(A)<n$.\n",
    "3. $(A-\\lambda I)$ is not invertible.\n",
    "4. $\\text{det}(A-\\lambda I)=0$, which is called <font face=\"gotham\" color=\"red\">characteristic equation</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a matrix $A$\n",
    "\n",
    "$$\n",
    "A=\\left[\\matrix{1 & 0 & 0\\cr 1 & 0 & 1\\cr 2 & -2 & 3}\\right]\n",
    "$$\n",
    "\n",
    "Set up the characteristic equation,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\text{det}\\left(\n",
    "\\left[\\matrix{1 & 0 & 0\\cr 1 & 0 & 1\\cr 2 & -2 & 3}\\right]-\n",
    "\\lambda\n",
    "\\left[\\matrix{1 & 0 & 0\\cr 0 & 1 & 0\\cr 0 & 0 & 1}\\right]\n",
    "\\right)=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use SymPy ```charpoly``` and ```factor```, we can have straightforward solutions for eigenvalues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "lamda = sy.symbols('lamda') # 'lamda' withtout 'b' is reserved for SymPy, lambda is reserved for Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```charpoly``` returns characteristic equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\operatorname{PurePoly}{\\left( \\lambda^{3} - 4 \\lambda^{2} + 5 \\lambda - 2, \\lambda, domain=\\mathbb{Z} \\right)}$"
      ],
      "text/plain": [
       "PurePoly(lamda**3 - 4*lamda**2 + 5*lamda - 2, lamda, domain='ZZ')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sy.Matrix([[1, 0, 0], [1, 0, 1], [2, -2, 3]])\n",
    "p = A.charpoly(lamda); p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Factor the polynomial such that we can see the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(\\lambda - 2\\right) \\left(\\lambda - 1\\right)^{2}$"
      ],
      "text/plain": [
       "               2\n",
       "(λ - 2)⋅(λ - 1) "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.factor(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the factored characteristic polynomial, we get the eigenvalue, and $\\lambda =1$ has algebraic multiplicity of $2$, because there are two $(\\lambda-1)$. If not factored, we can use ```solve``` instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 1, \\  2\\right]$"
      ],
      "text/plain": [
       "[1, 2]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(p,lamda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or use ```eigenvals``` directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ 1 : 2, \\  2 : 1\\right\\}$"
      ],
      "text/plain": [
       "{1: 2, 2: 1}"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.matrices.MatrixEigen.eigenvals(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the eigenvector corresponding to $\\lambda$, we substitute the eigenvalues back into $(A-\\lambda I)x=0$ and solve it. Construct augmented matrix with $\\lambda =1$ and perform rref."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & -1 & 1 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\  \\left( 0\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  -1  1  0⎤      ⎞\n",
       "⎜⎢           ⎥      ⎟\n",
       "⎜⎢0  0   0  0⎥, (0,)⎟\n",
       "⎜⎢           ⎥      ⎟\n",
       "⎝⎣0  0   0  0⎦      ⎠"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A - 1*sy.eye(3)).row_join(sy.zeros(3,1)).rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The null space is the solution set of the linear system.\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x_1 \\\\ x_2 \\\\ x_3\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x_2-x_3 \\\\ x_2 \\\\ x_3\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "x_2\\left[\n",
    "\\begin{matrix}\n",
    "1 \\\\ 1 \\\\ 0\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "+x_3\\left[\n",
    "\\begin{matrix}\n",
    "-1 \\\\ 0 \\\\ 1\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is called <font face=\"gotham\" color=\"red\"> eigenspace </font> for $\\lambda = 1$, which is a subspace in $\\mathbb{R}^3$. All eigenvectors are inside the eigenspace.\n",
    "\n",
    "We can proceed with $\\lambda = 2$ as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & - \\frac{1}{2} & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\  \\left( 0, \\  1\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  0   0    0⎤        ⎞\n",
       "⎜⎢             ⎥        ⎟\n",
       "⎜⎢0  1  -1/2  0⎥, (0, 1)⎟\n",
       "⎜⎢             ⎥        ⎟\n",
       "⎝⎣0  0   0    0⎦        ⎠"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A - 2*sy.eye(3)).row_join(sy.zeros(3,1)).rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The null space is the solution set of the linear system.\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x_1 \\\\ x_2 \\\\ x_3\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "0\\\\ \\frac{1}{2}x_3\\\\ x_3\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "x_3\\left[\n",
    "\\begin{matrix}\n",
    "0 \\\\ \\frac{1}{2} \\\\ 1\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid troubles of solving back and forth, SymPy has ```eigenvects``` to calcuate eigenvalues and eigenspaces (basis of eigenspace)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left( 1, \\  2, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1\\\\0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 2, \\  1, \\  \\left[ \\left[\\begin{matrix}0\\\\\\frac{1}{2}\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛      ⎡⎡1⎤  ⎡-1⎤⎤⎞  ⎛      ⎡⎡ 0 ⎤⎤⎞⎤\n",
       "⎢⎜      ⎢⎢ ⎥  ⎢  ⎥⎥⎟  ⎜      ⎢⎢   ⎥⎥⎟⎥\n",
       "⎢⎜1, 2, ⎢⎢1⎥, ⎢0 ⎥⎥⎟, ⎜2, 1, ⎢⎢1/2⎥⎥⎟⎥\n",
       "⎢⎜      ⎢⎢ ⎥  ⎢  ⎥⎥⎟  ⎜      ⎢⎢   ⎥⎥⎟⎥\n",
       "⎣⎝      ⎣⎣0⎦  ⎣1 ⎦⎦⎠  ⎝      ⎣⎣ 1 ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eig = sy.matrices.MatrixEigen.eigenvects(A)\n",
    "eig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To clarify what we just get, write"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue = 1, Multiplicity = 2, Eigenspace = [Matrix([\n",
      "[1],\n",
      "[1],\n",
      "[0]]), Matrix([\n",
      "[-1],\n",
      "[ 0],\n",
      "[ 1]])]\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue = {0}, Multiplicity = {1}, Eigenspace = {2}'.format(eig[0][0], eig[0][1], eig[0][2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue = 2, Multiplicity = 1, Eigenspace = [Matrix([\n",
      "[  0],\n",
      "[1/2],\n",
      "[  1]])]\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue = {0}, Multiplicity = {1}, Eigenspace = {2}'.format(eig[1][0], eig[1][1], eig[1][2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> NumPy Functions for Eigenvalues and Eigenspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert SymPy matrix into NumPy float array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 1.,  0.,  1.],\n",
       "       [ 2., -2.,  3.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(A).astype(float); A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```.eigvals()``` and ```.eig(A)``` are handy functions for eigenvalues and eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 1., 1.])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvals(A) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2., 1., 1.]), array([[ 0.   ,  0.   ,  0.408],\n",
       "        [ 0.447,  0.707, -0.408],\n",
       "        [ 0.894,  0.707, -0.816]]))"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eig(A) #return both eigenvalues and eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> An Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a matrix $A$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-4 & -4 & 20 & -8 & -1\\\\14 & 12 & 46 & 18 & 2\\\\6 & 4 & -18 & 8 & 1\\\\11 & 7 & -37 & 17 & 2\\\\18 & 12 & -60 & 24 & 5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-4  -4  20   -8  -1⎤\n",
       "⎢                   ⎥\n",
       "⎢14  12  46   18  2 ⎥\n",
       "⎢                   ⎥\n",
       "⎢6   4   -18  8   1 ⎥\n",
       "⎢                   ⎥\n",
       "⎢11  7   -37  17  2 ⎥\n",
       "⎢                   ⎥\n",
       "⎣18  12  -60  24  5 ⎦"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sy.Matrix([[-4, -4, 20, -8, -1], \n",
    "               [14, 12, 46, 18, 2], \n",
    "               [6, 4, -18, 8, 1], \n",
    "               [11, 7, -37, 17, 2], \n",
    "               [18, 12, -60, 24, 5]])\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find eigenvalues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ 2 : 2, \\  3 : 1, \\  \\frac{5}{2} - \\frac{\\sqrt{1473}}{2} : 1, \\  \\frac{5}{2} + \\frac{\\sqrt{1473}}{2} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧            5   √1473     5   √1473   ⎫\n",
       "⎨2: 2, 3: 1, ─ - ─────: 1, ─ + ─────: 1⎬\n",
       "⎩            2     2       2     2     ⎭"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eig = sy.matrices.MatrixEigen.eigenvals(A)\n",
    "eig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or use NumPy functions, show the eigenvalues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 21.69, -16.69,   3.  ,   2.  ,   2.  ])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(A)\n",
    "A = A.astype(float)\n",
    "eigval, eigvec = np.linalg.eig(A)\n",
    "eigval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And corresponding eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.124, -0.224, -0.   ,  0.816, -0.056],\n",
       "       [ 0.886, -0.543, -0.894, -0.408,  0.263],\n",
       "       [ 0.124,  0.224,  0.   , -0.   , -0.   ],\n",
       "       [ 0.216,  0.392,  0.447, -0.408, -0.207],\n",
       "       [ 0.371,  0.672, -0.   ,  0.   ,  0.941]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> A Visualization Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let \n",
    "\n",
    "$$\n",
    "A= \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 6\\\\ \n",
    "5 & 2\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$\n",
    "\n",
    "find the eigenvalues and vectors, then visualize in $\\mathbb{R}^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use characteristic equation $|A - \\lambda I|=0$\n",
    "\n",
    "$$\n",
    "\\left|\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 6\\\\ \n",
    "5 & 2\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "-\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "\\lambda & 0\\\\ \n",
    "0 & \\lambda\n",
    "\\end{matrix}\n",
    "\\right]\\right|=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "lamda = sy.symbols('lamda')\n",
    "A = sy.Matrix([[1,6],[5,2]])\n",
    "I = sy.eye(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 - \\lambda & 6\\\\5 & 2 - \\lambda\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1 - λ    6  ⎤\n",
       "⎢            ⎥\n",
       "⎣  5    2 - λ⎦"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A - lamda*I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\operatorname{PurePoly}{\\left( \\lambda^{2} - 3 \\lambda - 28, \\lambda, domain=\\mathbb{Z} \\right)}$"
      ],
      "text/plain": [
       "PurePoly(lamda**2 - 3*lamda - 28, lamda, domain='ZZ')"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = A.charpoly(lamda);p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(\\lambda - 7\\right) \\left(\\lambda + 4\\right)$"
      ],
      "text/plain": [
       "(λ - 7)⋅(λ + 4)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.factor(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two eigenvalues: $7$ and $4$. Next we calculate eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & -1 & 0\\\\0 & 0 & 0\\end{matrix}\\right], \\  \\left( 0\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  -1  0⎤      ⎞\n",
       "⎜⎢        ⎥, (0,)⎟\n",
       "⎝⎣0  0   0⎦      ⎠"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A - 7*sy.eye(2)).row_join(sy.zeros(2,1)).rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The eigenspace for $\\lambda = 7$ is \n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x_1\\\\\n",
    "x_2\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "x_2\\left[\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "1\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any vector is eigenspace as long as $x \\neq 0$ is an eigenvector. Let's find out eigenspace for $\\lambda = 4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & \\frac{6}{5} & 0\\\\0 & 0 & 0\\end{matrix}\\right], \\  \\left( 0\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  6/5  0⎤      ⎞\n",
       "⎜⎢         ⎥, (0,)⎟\n",
       "⎝⎣0   0   0⎦      ⎠"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A + 4*sy.eye(2)).row_join(sy.zeros(2,1)).rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The eigenspace for $\\lambda = -4$ is \n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x_1\\\\\n",
    "x_2\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "x_2\\left[\n",
    "\\begin{matrix}\n",
    "-\\frac{6}{5}\\\\\n",
    "1\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot both eigenvectors as $(1, 1)$ and $(-6/5, 1)$ and multiples with eigenvalues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "arrows = np.array([ [[0,0,1,1]],\n",
    "                  [[0,0,-6/5,1]],\n",
    "                  [[0,0,7,7]],\n",
    "                  [[0,0,24/5,-4]] ])\n",
    "colors = ['darkorange','skyblue','r','b']\n",
    "for i in range(arrows.shape[0]):\n",
    "    X,Y,U,V = zip(*arrows[i,:,:])\n",
    "    ax.arrow(X[0], Y[0], U[0],V[0], color = colors[i], width = .08, \n",
    "             length_includes_head = True,\n",
    "             head_width = .3, # default: 3*width\n",
    "             head_length = .6,\n",
    "             overhang = .4, zorder = -i)\n",
    "\n",
    "################################### Eigenspace #################################\n",
    "x = np.arange(-10, 10.6, .5)\n",
    "y = x\n",
    "ax.plot(x, y, lw = 2, color = 'red', alpha = .3, label = 'Eigenspace for $\\lambda = 7$')\n",
    "\n",
    "x = np.arange(-10, 10.6, .5)\n",
    "y = -5/6*x\n",
    "ax.plot(x, y, lw = 2, color = 'blue', alpha = .3,  label = 'Eigenspace for $\\lambda = -4$')\n",
    "\n",
    "######################## Annotation Arrows ################################\n",
    "\n",
    "style=\"Simple, tail_width=0.5, head_width=5, head_length=10\"\n",
    "kw = dict(arrowstyle=style, color=\"k\")\n",
    "\n",
    "a = mpl.patches.FancyArrowPatch((1,1), (7,7),connectionstyle=\"arc3,rad=.4\", **kw, alpha = .3)\n",
    "plt.gca().add_patch(a)\n",
    "\n",
    "a = mpl.patches.FancyArrowPatch((-6/5,1), (24/5,-4),connectionstyle=\"arc3,rad=.4\", **kw, alpha = .3)\n",
    "plt.gca().add_patch(a)\n",
    "\n",
    "############################ Legend ###############################\n",
    "\n",
    "leg = ax.legend(fontsize = 15, loc = 'lower right')\n",
    "leg.get_frame().set_alpha(0.5)\n",
    "\n",
    "###################### Axis, Spines, Ticks ##########################\n",
    "ax.axis([-10, 10.1, -10.1, 10.1])\n",
    "ax.spines['left'].set_position('center')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('center')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "ax.minorticks_on()\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=12, width=2, which='major')\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=10, width=1, which='minor')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Geometric Intuition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eigenvector has a special property that preserves the pointing direction after linear transformation.To illustrate the idea, let's plot a 'circle' and arrows touching edges of circle.\n",
    "\n",
    "Start from one arrow. If you want to draw a smoother circle, you can use parametric function rather two quadratic functions, because cicle can't be draw with one-to-one mapping.But this is not the main issue, we will live with that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4)\n",
    "y_u = np.sqrt(16 - x**2)\n",
    "y_d = -np.sqrt(16 - x**2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax.plot(x, y_u, color = 'b')\n",
    "ax.plot(x, y_d, color = 'b')\n",
    "\n",
    "ax.scatter(0, 0, s = 100, fc = 'k', ec = 'r')\n",
    "\n",
    "ax.arrow(0, 0, x[5], y_u[5], head_width = .18, \n",
    "         head_length= .27, length_includes_head = True, \n",
    "         width = .03, ec = 'r', fc = 'None')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, the same 'circle', but more arrows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4, 50)\n",
    "y_u = np.sqrt(16 - x**2)\n",
    "y_d = -np.sqrt(16 - x**2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax.plot(x, y_u, color = 'b')\n",
    "ax.plot(x, y_d, color = 'b')\n",
    "\n",
    "ax.scatter(0, 0, s = 100, fc = 'k', ec = 'r')\n",
    "\n",
    "for i in range(len(x)):\n",
    "    ax.arrow(0, 0, x[i], y_u[i], head_width = .08, \n",
    "             head_length= .27, length_includes_head = True,\n",
    "             width = .01, ec = 'r', fc = 'None')\n",
    "    ax.arrow(0, 0, x[i], y_d[i], head_width = .08, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .008, ec = 'r', fc = 'None')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will perform linear transformation on the circle. Technically, we can only transform the points - the arrow tip - that we specify on the circle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a matrix\n",
    "\n",
    "$$\n",
    "A = \n",
    "\\left[\\begin{matrix}\n",
    "3 & -2\\\\\n",
    "1 & 0\n",
    "\\end{matrix}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Align all the coordinates into two matrices for upper and lower half respectively. \n",
    "\n",
    "$$\n",
    "V_u = \n",
    "\\left[\\begin{matrix}\n",
    "x_1^u & x_2^u & \\ldots & x_m^u\\\\\n",
    "y_1^u & y_2^u & \\ldots & y_m^u\n",
    "\\end{matrix}\\right]\\\\\n",
    "V_d = \n",
    "\\left[\\begin{matrix}\n",
    "x_1^d & x_2^d & \\ldots & x_m^d\\\\\n",
    "y_1^d & y_2^d & \\ldots & y_m^d\n",
    "\\end{matrix}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrix multiplication $AV_u$ and $AV_d$ are linear transformation of the circle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[3, -2], [1, 0]])\n",
    "\n",
    "Vu = np.hstack((x[:, np.newaxis], y_u[:, np.newaxis]))\n",
    "AV_u = (A@Vu.T)\n",
    "\n",
    "Vd = np.hstack((x[:, np.newaxis], y_d[:, np.newaxis]))\n",
    "AV_d = (A@Vd.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The circle becomes an ellipse. However, if you watch closely, you will find there are some arrows still pointing the same direction after linear transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "\n",
    "for i in range(len(x)):\n",
    "    ax.arrow(0, 0, Av_1[0, i], Av_1[1, i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'darkorange', fc = 'None')\n",
    "    ax.arrow(0, 0, Av_2[0, i], Av_2[1, i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'darkorange', fc = 'None')    \n",
    "ax.axis([-15, 15, -5, 5])\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the cirle and ellipse together, those vectors pointing the same direction before and after the linear transformation are eigenvector of $A$, eigenvalue is the length ratio between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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78z6pz+rCBdYlT54MzJvnOGkwTWZ9t27tOKYg1CUlhUBRNuAbclfDiBALP17sdsYjL10CpkzRD/KgIArTM8/Qnbp1K0uFlOi4uzOB6Z136FZu04aCceAAfx88mNnHn3+uu2O1aEFru00bWniXL+vM4ogICsz16xRiw6BYXblCizMyUsee09N1/FeJZHUs4sqE2DT1Qg/KFVyeRazi00qI7XZ9Txo14s/MTP7z99cJahkZvD4/P205m6a2nF97jeOcPctFLzp04DGSkljS9Ze/ACFlDzo1Mbl0CVi7liLs78+xVTzZbudrp07x/EWIhbulIAO4HQvcPsefaeeA9Fgg4woQ2hmYcrzqMSpBXNPCjxc/PyZlRUZSAJTFFxRE8fDxYSnOlSusy7WuNpSVRbHct49iceoUXan9+rFBh7u77lZlXZZQZTxfvKi3KctRCROgLUwldIah63XT0/lTiWRlFnF1XNPKvW6NvVbHIk5Lo6iHhmoBV9cQEaHHUtZw69Z6m3JTq85g993Hki/DoBv65k1mogcFUXyV2z4vj+e2ejUnQ+Hh/KyU6Kv649xcnmfDhhCEWnPoL8DMMGBWOLD9deD6dsAzAOj4LND5FcArABjx6V0fRoRY+HFw8yZdxs59oBs21Fbs/Pm0QJUQA1qMExMpEKdOMaFo9mwK+LJlfL1nT+5/8qQeOyqKP2NitJCoRKzLl/ViD82b86c12UgJcWUJW3VlETu7pa1jqmOUltIittn0BKA8t7QSYnVNgKMQK9TkRN0jgK7m/HzGiCdO5D1+/nlg+XL+272b6yUfOcKELhVLVkJcWMiQgYcH8OSTFGxrtzG7nZnt1qUjBaEySgqAxn2AN7KAZ44CDy8E+v4G8KgHHP4LMH4dENbnrg8jQiz8OLDbmdgzezbdyIqGDekC7d6d2b0LF1Ksrb2iASYeRUdTjDMzWavr46PFUSVdnT6tFy8ICeH4OTlaoHx8KCClpXpbYCDFLStLH7c6CVt+fvyZmamFvjYx4vKEWFnESnSVFR4aqq3a8hK1nOPDpaU6/qsWpSgtLV+IT5zgz27d+NPXl/evpIT3KiMD2LiRrmaVHQ5wu5cXJ1IhIYzhZ2RwEqEs9cJCTsQOHLhzMiYIFdHmUeDKOiDH8v8w7ltgw9PA2NVA0/51chgRYuHHQVgY3cUDBwJffKFdww0bamGOimIt79atfD0jgwk/8+bxQb54MS20Bx7g/ocPa6s2IIAWX2kpY50Kq1WsUP2alaVoGHe6pxs00G0klbA7C7FhUMQB7TavjWu6OhZxdRK18vN5Lz09tUs4Pp6u7/BwnWR17RqP2aSJdimrvtJubtqlD7CeGuACFGPHUmyHDGE7z507Kfw3btBabtOGjUZsNp6HOofMTIYe6tXjfVaWtHDvU/odrdiVdR3Y8hKwsCtglgKH/8rt17cD6ycDY78CwgfW2eFEiIUfHnFxjN1a64Dd3Gi5NWhAt+XatXzIh4Y6WsiRkSwrOnYMeP99ikNKCkVRWX5NmvCBnpfnKLrKkrO6p61xYnU+ykWrhBjQrlwlxCphC6DFDlSvhOm7soidhdg0tRCr+6IWwGjeXB+3Mre0VXBPn+bPjh31QhXZ2Xp7jx78qRbKME2GCdaupaUbEaFXhgK0EN+4QS9Ily7AmDG04q2Z7gBzAA4cgPAfTmEWcH0HcPg94OuJwKwIYPHdu4UdyLkJbHsd+Lw5EP05t/X4CXB1PXDwXWDdk8AjK4DwwXV6WMmaFn54JCXRqr12jW5K5cZU6+oOHsxWkUuWsBGFWvmnsJAP/l27gDffZMcsw2D5UUwMBVnFHPv0oWgeOsT1fQ2DXbG8vDgRUOVJoaG6POnGDZ5DWBitw+RkWmuBgRUnbMXHUzyaNdMimJqq97GWMIWFaTFVDTqcE7KAioVY3afSUrpv3dz0eM5CnJnJ9wUF6fdZE7UUzkJst9/pljbNO93SAHtdAxRR1YrTbqeXAmDf7nbtgK5dKcpffslJlLq3np78jMeN4363bvF+qfNVJU47dtBt3q8fhP8gsm8Al78Bbh3mv8xrQMOuQOPeQMNuFMdh79fNsXKTaPUe/7fe1vV1oM+vgHpNgEa9gK0vAuO/BpoNrfn4BRmVviwWsfDDo1UrPrhDQthqMSGB28PDKYYAezFPn07BiY1lMtA//sEYZEQEH95+fnyoq57QSgAAZvkGBDAJTI3p7q5jxeUlbSnr2TDutIobNqRwJCfrUiLnOLGPD4UxJ0evXlSVRQxQUE1TW+RVuaaVmzswUFuYzkJcnfhwdjb38/bWJUTXrnGSEBam+2EnJHByUb++9gyUlDApC+CkRxETw3Np2JCfgc3GidXAgcwBeO89xvl37eJqTlOnUoQBfk7KGs7Lo0hfusT4v4pfC/85HPsXcPx9oEk/4OHFwOsZwOR9QJ/fADFfAIP/F2gz4e6OkZcK7P4F8FkTLcKdXwJejAOGf0gRBoD2k4HXM4GI+2s2flYcsOMnwKeVZ++LEAv3NsXFjm5XgJaouzsTsB58kA9c1Xzjxg0tSO7uFA1lIb3yCsUwNtZxneH+/fnAV804AIpb7978/eBBvW/Xrvx54oQWvPKyp52F2DC0CKljO2dOG4aup1U1vc5NPcoTYmu/ZqBq13R5pUvKCldC7BwfLi7W5920qeO1tW6tRb+yJK2uXbXwnz1LsYyI0CJumowFAxRftW9xMVeJAhh2aN+eE5XISMdGLfHx9CzcuMEJWmgoW3ImJZUvxNZ7KHz/dHsDyE8Fmj9AS9jNAyjOA9aMAdpMBLq9VvuxC9KBvb+lAB95DzDtQIfngBeuAA98BgRE3PkeWw0WGUk6Aax/Cvi8BQXeXlzp7iLEwr3N2rVsnGGN8xoGH6yXLvGhPH06a323bOFrt28z9rtqFTOh//Y31qSGhDARCOC+Srj8/LTo7t2rj9O9OwXm7FktXmFhbG6Rnc3YI0DrLSSE+yjrXD34L13SwugcJ1Zu8MREvY9qAqImBNWxiJ3jxFUJsXMzj8JCWuHe3nrS4hwfvnmTPyMitPBXxy1dXKzjwMqbYJo6SctqDcfG8nNu0MBRyA8e5Pm1aEEruWdPJnP5+jIx78QJHuf6db5/6VJmyI8cyYQ8u92xzKmggCVq//73nZM8oXys+Rh1QUkBELsUKEwHzi7gNnsJsG4SUL8dMPDd2o1bmAUc+B/gs6bAoXcpkO2fAZ6/AIyaCwS2rP05myZwdROwYgSwqDvP37BxQjH9cqVvFSEW7m3Cw2k5zZ/PlYyUFdq6tS6bCQ6mGCtrd9Ystq6MiaGlZ+253KcPBSg+nvsq+peVKZw4oUuMfH21BazcqIZxZ9KWYdyZPe3nR0uvuFi7tpVLV7l4VYKYaTLGDFRcS1yZReycOV2Va9rZIrZ21HIuXVIWsbNb2m6/U4ivX+dnpZLmAC7YUFxM61VlUMfHU9gDAiisgKM1PGiQPve8PL39gQf0+amM87Q0Ju599BHF/do1fhfUuJcvc1JkbTQycyY/kyZNZKnFiijKZvx22xvA3HbAiQ/qZlzTBC6uAubdB+z9NS3V4/8GLn0NfPsqUFoIjJztuOhHtc43Bzj0Vwrw/v8GSvKBtk8Az8awNrh+m9qfc2kRcPYLYEFnYNVDwPVtgHcwMOBPwIxk4P4PgKDISocQIRbubaKi+CCfPp0xwi++YM1ry5Z8oKvyIpuNMc/GjWnJvvYal/EzTcaFre7q4cP5+7ffaosoIID7A45WsbLYjhzRCVGdOvHn2bM6acoaJ1bHci5jatKED5gbN/RYzu5pZyF2tohVxrGKMwN3NvWoqUXsHB/OzaVY+/pqsXZO1EpIoCUdFqYTrVSMvLLaYcCxZEmd48WLtMKDgvT9BSjCxcXMwFYucYAekIQETsJeeYUx/8hIfgfcLTmqSoiLi7nIx6pVLIFq3NjxPH/s2EuBxMPAwXeALwcDM5swfpuTAOQlAS0fvvtjpJwGVgwHvn6MsdUmA9hE45GVwPpJQNIxYOxKuqirS3EecPQfwKxmwN5fAcU5QOvxwNRTwCPLgAbta3++hZnAkb8zw3rTs0DqGaB+W+CBWcDLCUDf3wI+DaocBhAhFu4l1Hq4VgIC6PZNT2e8r107uqrPnaO78fp1Cts33zBO/ItfMG5sswH3309X64ULFHFFp058EKelaaEA2D8aYDavshobNaLoFxTQzQ3Q2m3fnoJ75ozeLziY2cbKjescJ3Z31zWuyoXtnLBVlUVsGBRUu91xEgJUX4idLeKKErXCwng8u11bxOr8q+OWzsigBerpqS3UzEwKts3GCRNwpzWszvv2bR2fV5MngBOFLVv4++jRvK+RkcAf/sBty5bxsyopoYXs40MvSXY2MGMGXdwqrOGMc6OXHwP7fsdkoy3TgYLbQJ9fAzOSmEB16wjw0KK7syjzUoCtrwALugDxO5ggNXopMGkP0KgH0Hw4/350PeBZzRW2SgqA4x9QJHf9DCjMACJHU9jHrWZ/6NqSFQ/s/Bnvye7/AnJvAU0HAuPWAs+dAzq/CLh7Vz2OBRFi4d7ANOl+/vxzLVKKqCj98O7fn4J86BDFYdUqlrXExvIBbW0j6ePDZQ0BrperGmfYbLppx/btentQkLbc9u/X4yir+NAhbe1ak7YACpZz7+mmTWnBJibqbk/OceKKLOLUVB7Lw4PXUVDguCQjUHFTj6pc01VZxM6JWsnJPHajRjqGrBqmKCGOj9drFKuEM+W679xZd8BSJUtdu+pEq6tXOZny99dxZICfDcD7r2LnAEvXiop4v61JWLm5HCshgcI+cyavbdUqJn9NnKgXlAgL053L1HtXr2bc2Fo+9mMgOx6IHANMiwaG/hNoOQqweQDrngA6Pg+0GlO7cUuLmBn9eXPg9GcADKDfH4DnLwL3TXJ0P7ceB/g1rmgkxzFPzQRmRwI73tLJXpMPABPWUdhrS/IpYMMU4PMI4Ng/eKw2j3HsSXuA1mMZE64FIsTCvYFh0GoqLWWyzYYNWkCiomjRKkuvUSNaQmpBgldfZVcmgJaxtTdz584Uv6wsbXUBfIC3akUXr1V0Bw3iz8OHtXi2bUuRTkrSQt+mDR/kN2/qhhzO7mmb7U6r2DlOrFY1unmT7/H0pCAVFmr3s7NVrMSwon7Tzhaxcp/X1CJW1rpzfDg3l+fr4aHLhcqrHVZCrCYtxcXllyxZrWHlVk5IoLfBw4MiqoiL47hubvR8KEyTiX3FxTzejBn8abcz5NCxo37wx8Q4nuexY8Ann9AaDglx7C72Y2DAO8D5L4FUS/OaPb8APPyA/v9duzGvbAC+6ATs/H+M1943mSVD/f8b8PCt+v3OlBYD0XOAOa2Bb2cAuYlA+BDgyd3AxC1Ak761O0/TBK5tBVY+yC5b5xZxe5cZnDCMXVn7sS2IEAv3Dt26UXxmzKCYfPwxH8YBAaxBvXaN/3Hi4rh84VNP0Tr29eWDtVMnWkpff60tV8OgaAOM/aqkKIANPQDWDyvRDQ6meKslFAEKqhIO5Sq12bTAKMFp3JjnmZGhrUpnIVau3evXeQwvLz74i4t1v+eq4sRVddeqzDVtmo5CbJpVly45x4dVklzr1rqG2Tk+fO0a70NoqI7tRkfzXFq21BOQuDju6+envRGmSasXoAgry7W0FFi/nr+PGOG4hOPRo8xi9/enF8RmY+3xr37FrO29ezm5KSmhNd++PSdQc+fy85s6lZ9d9+41TxT6vkg9A+z5NbC4N+tj64JrW4El/Wj9bZwC5KcB55YCl9bSJV1TCzAtFlj1MLB6NJB+AWjUE5i0Dxi9BAioRetReykQs5DJXVteoPXepD/w+DbgiR1A+KCajwlQ2M8tBhZ2B74aCcRtAbyCaLHPSAZGfALUb13lMNVFOmsJ9w6hoRTC+HjgkUf4c906JuaEh9Oa2ruX7kfAsZsUADz8MB/GFy/SZaxikA0bMv67bx8f5NOm6RaTnTvzQb1zJ1skArTMTp+m6A4YQKHv1o3JXbGxFMz69SnE+/bxQT5iBEUpKorbYmKYnGUVYrudYtiokV7HOCxMx6sTE3n9DRpQnNLSKH5VZU5XZhGbJi1iw6C1WVjI++bnx9dzc7nN35/WeFERj+vuzgyvRa8AACAASURBVHNREx9AC7FzfDg+nhMZ1WUMcEzSMoyKS5aUNTxggHZfX7zI669XTzdbAfh+1dpSlZsBjCVv3Mjfx493bOVps/G+bdvG70/nzrR69+9nt6777+f3pLCQn60KWfynkHWdZTKxS4D824C7F+ATAngH3d24hZmMrUbP5t8RwwH/COCbx4HUaGDit4BPcOVjWClIZ9mQaprhEwIM/jvQYWrt3LmmHTi/ghnQ6WX5HY17MVO5+cjaT5YKs3jNx/7BdpcAENQK6PkzIGpq7az1aiAWsfCfR0EB48HWphiK7t0pvACtx5dfphv40CHu37Ill8gDaPkqtzBAl+24cfx9wwbHxJshQyg2167pBCuAD2KAFpWyDENDGX8sLdXi4e2thV25V0NDOUHIz2dCGHBn72l/fwptQYFO4qpunLi6FnFlMWIV/1ZrEVcVH1bnoDK8MzIoskFBuge0sxA795YuKND3uHNZ0kxcHD+roCC6+gHGhS9f5vWoZSbtdk54ACZoKXFWYgpwwmS95rVrtQvaGjMuKeGaxyUl/OzGjqUb+tw5XtOrr7LHtWHwfCMjHePG6hwXLHDMPfiuyU9jHPTLwbTYMq8Awz6gBViQATw4H7DdhY11ZQMtzOjZgJsXs4AnbqUV6FGPx2rYpepxANb+npoJzG6pRbj3L9k4o+OzNRdhVd60oAszqdPPA6Fd2XryqUNAiwdrJ8LZCeywNbMRsOunFOGwfsDYVcBz54Eur3xnIgyIEAv/iXh58UG4ZQsTai5e1K7kqChaWNYs4eJiCtrbb9NVGRXFvsGmydaVqh0kwId8t258+K5dq8f19KTFDNB6UiIWFKRriNWDHtCx4gMH9L7Kkjt6VAucs3s6LIxj3r6tJwlVxYlrmjldE9d0bTOmK4oPJyYyfNCwoRZm5/jw2bMUxnbtdGmTcun37q3P12oNe3ry91OntNVrTdzavJnX1a2bY69rlbQXFHSnNbtpE6+nUSM2+Gjdmt+hTp14Ddb6cqsHRd2X5cvZte3q1TsF+ruitJiidmUdrbRXbrITVPggZjX3+RXQ4L7ajZ1/G9g4jW7j3FtAi1GMg3Z+scxj4g1M+JrtHqvD9e2cKHw7gxZ26wlsbDHoL9XPflaYJuuWF/VgeVPqGaBBB5Y2TTkGtHqkdgKceoalR7PC2WGrpIDlTZP2Ak/tZwvNmnTUKo+0WMbCK0GEWPjPwzAopOHhtHo2b6bVcfMmH8hRUXwgFxbSzbt9OzNerQvUjxjB96el0X1t7fzz4IO0+K5e1dYrwGSwNm34EN6xQ28fNIjHPXdOW6mNG1NIior0QvMhIXyYFxXx/AAmAdlsTCbLyXFs7qHiphUJ8fXrPG91XYmJ/Lu2FrGzENtsd58x7RwfdraGb9yguIeElO+WBujKj43leSqxS0ykF8HTU7uZra0sR4xwXOHp7FlO4FRcH2C8X5UxTZigxRxgPProUR7ziSe0Ze3lBTz9NAX6m28o+rdu8bOLjOTP9euBOXPoFRg0iN8DlQn+XePmAXR4lq7ZyNGAW9k1nfiI1mf3t2s37sU1wLx2QMwCwN0XGDUfeHRD7eK2GVeAtY+yJjg1GgjpyJjtuFVVNra4A9MErm0GlvQF1owFkk+wVnf0UmDaaaDtY7Wzqq9vB756iAljZ7/g9s4vA8/Fsryp6YCajelMSSEQ+yWwfBgwvz2zwytBhFj4z6RLFz6M69eni7BjR2ZLr1zJB+LRoyxlUg/1r7/W2b8AH7ATJ/LBGh2t3dkARWf8eP6+aZPuHGUYtIwMg5aUdbGFoUP5+9atWtRVtu7+/doCdi5l8vbmuQO6laNz7+lmzRhzvXGDk4CAAFpwOTkUKT8/Wqi5udymFktQJUzVjRErl7S1vrimFnFFQqzc6c5lS1Zr2DD0KlS+vrqhiZoMde+uz0MtsNG/v25SYm1lqd5bUsIwA8CWlcoytdvZptI0OalT56fu25o1/H3CBMcsaNXgJSeHnpf58zl+hw48p08+4f18/XWe25Ej2mNSHqrt4doJQObViverCS1GAVc3ApfX8u/0i4y/Pjiv5tZbXgrbRn49gaU+rcYC0y8CHabVontVNrDnV8CcVsCl1YBnADD8E2DKiZovlgBwycMvBwFfjeLqS4EtgVFfAM+eLStvqqF82UuYaLaoJycJ1zbRMu/7O9ZFPzATCG5X8/O0knG5bBGJMK5bHL+TSV49f17p20SIBddTXp9ad3daQgcOUDB69ADeeIMuyW++oXXTvz8zqJs1o2CsWOHYGzgoCHjsMf6+bp12qwIU81699ANbiVRwsBZdqyXdu/edrS+bNqXgFBRoMWndmg/21FTda9paU2yafF9gIM85OZkPdiVcKuO4ojhxYiL3Dw7mOWdmatGsrkVst9euq1Zpqb6HoaGcGKSm8r0hIZwIxcdz7IgIR7e0ig8rF32XLtyvqEjXDqtJTHIy3+furrfl5pbfynLfPk6kmjZ1dB3v28cSp5AQHecHaFWr70nPnnqSpDh4kJM2Dw9mSk+ZwmMdPsxJxIsvMuva15deDl9fnelupbQYiFnEkpcNT7PtoUcN3bHOmHYK7uqyLP8NU3iMTc8B/X4HBLetwVgmcH45MLctcH4ZRfPhJcC4NXrFoZqc15n5rN09/Fdu6/428OI1oOuMmserb+wFlt8PrLgfuLkPqBfOtpbPnWdyV03HK8phF7DZkcCGp4Dk40BAC+D+j4BXEoEB/wP4Vr46UqWUFjNuvXIky6eOvMfktPAhtNxfuQUMea/SIUSIBdeSmAj861+6fMRKz54UPSUOnp4UMDc3Jl11786H9aRJFI4rV2jhWmnbljHG8uLFDzxA6/L6dccVlAYMoNAlJGhLuqLWl8oq3rePD3nDcLSKASaQBQbyQZ6QUH7v6arixJUlbCkrMDNTW+FA+TFiNeFQ9biVWcTW0qX69fXCGmFh/Ays1rBh6IlHq1Yc/+ZNnlODBpxA2e131g6fOkUxbt1au3eVNdy3r66JVq0sO3bU5U63b+sQwpgxjn2wlQt7/HjtdgZo7apsdNXMRXHhAsMgAL9ToaHcb/JkxpHd3R1Lovbv52TQajkW5QAbfg28Hwbs/Qcw6K9AxAig1y8A37twX+enAatGM0sYoIg8dYDxV5sbFxaoLrm3GGdd9yQ7TrWdyEUP2k+uuRWcsB9Y3AfY/Bwt6pYPAc+eA4b9C/CuX7OxEg+xXnfZIHbY8m1Ei/qFy0Cn6TVrbQkAOYks55rZGNjxNkubGvcCxiwHpl/i6k0edxHbz4orW8GpKe9n3FYms/X4Ce/Bkztpubt7VTmUCLHgWho04AM6Ohp4/33Ge9V6uL6+TJxRbt5Ll5hgpeK/Cj8/xvXc3WmZqpit4v77abXcvk1r2pqgpVzUW7boGmJ3d524tWWLPp/OnXUpkRLoiAgKbV6e3talCx/+Fy5w3/IWgnBu7mEVYtN0jBMDlSdsGQaFHuC5KlFVrnqra7qirlpK8KwWcWYm9w8O5hjOiVpVxYettcOGwddzcxlbbdSo/JKltDR+F2w2upQBfm5qP2XdmqZ2SffurScqpaXa7TxokOP35NQpfkbu7sDjjzv2nE5KYutLgJ+9Nbva25vLK0ZHc53joiJee26ubs2ZkwSsegX4MAy4sBHInQA8uIaW1s29QI9axm4BtpFc0IWu1HpNgKcOUkRCO5f1Yv6qem5a06QFPacNXcfe9YFHVvCfX6OanVNWPJf5+3IAkHSULS4nrGdcuabJYknHgdVjGAeO2wJ4NwCGva8tajfPKodwIO0csHk6lzg8/BegOBeIfAR4chczq9s9XvsELHspk8ZWjeYSh4feBfJTWLs86gvWGA/9Z43vgQix4Fo8PWlV+vsDL7xAQfvoI1oumZl8GB8/TjfxqlUUhg0bHN3MAB/sqmxpwwbt4gUoIo8/zgfqmTPaFQrQmlMP/NWrHVdvioqiBa3KZQxDZ97u2KGta2UV793LmKWXF13pgJ4UqAzf06dp2YWH85pTUzkBCArS7t5bt2gd+vhQmHJyql/ClJVVuWu6Jn2maxIfNk0dH27TpvxsaeckrStXeP0NGmjxVtZwnz7a0i+vlWVsLIXd19fR9bxrl86EVktaArzHa8tiqo8+6tgSMycHWLyY96ZXL8caZIDCu3w5Xz96FJg3j3Xl/frpErbPJgNxK4EH1gD9PwNaDuF92f1LoO/va2d5mSZw8lM26MhJYH3slFNAmKXOOrhd9Szt7AQmO22cwoUP2j8NPHeB1nBNKM6je/zz5qxfdveh8Ew7A0TWcOGHlGgmdS3qAVxZD3gFsrb4petA9zdr1q/ZNIH4XcDqR4D5UcCZudzecTpXWJrwNRA+uPb1xdkJZdcdwft4dQPPr+trwNTTwOR9dJt7+NRqeBFiwfX06MGHflYWXYyvvkqhmDmTLslmzViv+uabdEcXF3OVJSUUirZtdVvDL7907JIVEKDjxevXa1EB+CAPCaEr1bqy0qhRPI8TJ7ToWFtfqs5aLVrwHLOztcWrHubHjlGw69en5VxURBEpr/e01So2DMc4cWAgxTI9neJZUQlTdnblrunKhLi0lKLk5sa/KytdKiqim91mozAnJ/O9DRrwWhMT+ZkFB3P/vDxmnRuGjstaS5YMg9d28iR/VwlQ5bWyLCrS1vCoUfp6VQ9pgElYyuJVQmq381hqYmAvBY7+G1j4c373IiOZrGelpITfpRs3OFF6/XVawenpvN7332f2/YQPgAbhQPZensPw4exKlX2d/ZhrSnEusHEqsO1V/t3397Q2a+reNk22fpzbmiVPPqFcnODhRTUbyzSZBTy3TZl73GSW8YtxdMXWxGpNOwd88ySXDby0mpOUge8CL8UDvX5Ws3pdewlj3Uv6AMuH8ho9/LgwxSuJwIOza7/CkmnXiXazwnndOTfp3h45G3g1FRj+ERDaqeqxqkCEWHA9bm5MkNq2TWcBjxxJQb5wga7PKVP4wB0zhgKWn08xzsx0HKtvXy3Wixc7LgfYpo2u/12+XIuQhwcf3ACtLyU4AQE6Lrx+vbaWnVtfGoYWiT17KGjBwSxrKSnRlqDzQhAVxYmVZWl1T6tOXwDPr7ISpsqypitb8EG18QwM5PGsQmyauuFI48aOayi7uVWdLa0yxjt00Jb+xYu89+q+7NvHnz176hh1ea0sd+3idbZooZdELCmhRwMAhg3T7nOAop2SQpf4yJHclnySrRt3/QRIP8drfOIJx9phu51Z+leu0GMxZQot8CFD2D519252eJs0CQhvzjVoD/8NCI4BGjdiP+aBf655bPP2ecZdzy1iVu+jG4EBf6y5OzUrjhnHW15gfWyH54Dnz3NxgpqQdIzZy+snU4iaDQWmnGSWsW9o9cdJv8QEs/lRwIXltCj7/YFLBvb5dc1qi4tzWbI1pw1j3beOsPPXsPeZHDXw3eotElEeuUnAob8wuWvVQ8ClNUwQ6/wS8Mwx4OnDjFnfTXzZCRFi4fsjI4MWj3PrSYAP1MJC/UAHGJ9t3tyxjaHNRtdi69a0YhYs0DFcQPeObtGCx1u2zDGTetgwjpme7thzumlTLaarV+sSnz59mGiUlKTjlGFhdDWXltJFCfB8mjThxECJjop7Hj7M40RF0Uq7coXn1qwZG1okJ1Momjfn9V2/ToGsLE4cEMB909N5HtYSJlUvm5fH41bXNa3iw2osVdbVoAF/Lynh756elceHnXtLm+adkxHlsu/Rg678rCwdMhg4kD9VK0t/f/0dSE7Wgj16tHY1bt9ON3eTJvr9AL9vJ09S8B9/HLAXcAm7rx4EfAYDpg9g9GaOgbX1pWny+xEbywnA1KmOiVqhoZwUrl8PZNwEVj7ABKNSb8DczxpVmwfQ5lE93tWrjiGT8riwkpZi2ln2YZ4WzdWOaoJpp0t7ThvGXOs1oZiPmluzBKrcW4y1LurJ7OWA5sDYr4DHt1e/sxYAZF7jOHPbcHJh8wD6/AZ4+SYXefAKrME5JXFZxplhwPY3gKxrXFFp9JdM6ur+JuBZr/rjKUw7ELcN+OYJJnft/TUnMqFdgBGfAq+msXFKo+5Vj1ULRIiF74+4OCbS/POfjAFbXcdqfeBt2yjUa9YwOSYrS9foKlQThogIWlaLFmlBsb5evz6PaS1DstlYX+zjQ6vNmtg1ZIju87xrlx5L9Zjetk3HUIcN40/V+tLZKrbb6YoODaWIKetPxYpPnboze9rdXScJXblCwbfZaIkWFjpaxIahG2SkpztaxIbB6zNNimd1XdPq2sorXaosPlxYSME0DE6Abt3iOQUFcf9bt3hP/f3p/i0spMse0C58Ja7du9Mit9u1NXz//bx3pqkXdRg4UF//9et6hawJE/S1JSdTTAFO3m7vA77oCOQnA32/As5dA0obA5NfdYwZmyaz70+e5CRh2jTH19U+aWmMHc7rzYxf7xZA5D+BSbvYGnLoP+m52b+feQ9ffOFYz26ltJjdl755nAssdJnB7k4BzcvfvyIyrrBGdturgL2Y7uNnz9VMzEsKgcPvMQ58Zi6twYF/ZrOLNo9WP86aFc91hme35DiGjfW0L98EBr5Ts0nB7fPAlpcokgffYc1yy4fZ1vPpI8B9T9aurWdeKnDkf4G57YCVI4ALKwAYbJry1EHWQHd5BfAKqGqku0KEWPj+6NyZVmCvXnzALVjAxJfTpykY7drxgfvppxTf0FC6QL/4wtHqBWiVPfUUrcTERLYatFravr60cjw8aI2peC5AQZhYlqSycaNe39jNTbuo9+xxdL927cpzVOUt1taXKpmrXTsK+e3btAjLK2Wytrw0zcrjxG5uOk5840blmdOVNfWormvaahGXlvI6bDYKs1WIS0t1WVV4uF5kIzKS99taO2wYjklaNhv/LilhTD84mC5xNSFS1uzJk5yoWVtZnj7N4wYEOMaLlUt65Egtzta4cI82wKXfAzt/AoycA3T5K/DNdsDjJNB5OicPVnbt4ufl5kZ3dEOnGlM1ITiwHvCdB9gTAEQAOVOA4ROYKd3jI+BQEvDBB5yEDB7M76RyjVvJTmAHpmP/olg9tJB9natR9qLPyc5a2blt2ETCP4ILMzwws/oiYppcVWl+e7rVS4vY2OPFOLbOrG7yVE4isO0NJjad/ozbur9NF/SQ96ofmzZN1hSvGVfW+/pzbu/wLJPDHl1PN3lNE7BME7ixB1j/NPBpKLD750DGJaBBFF3br6UBo+YxKe57WmlLhFj4/lBu42PHKFBvv02X46lTrCXeupUP4s6dKZTPPactqnnztMgovL2BZ57hw/z6dZ3ZqggJYfwOoJv7/Hn9WqtWOqt2+XJd6tO4sc7CXbNGi/sDD1D8z57V7sVBgzihiI3VcVwlELt38z98ly7c5/JlCkt4OM8rPZ2i0qwZXZ9JSbSsVcco1V/b6p4OCaGQJSfzvKxCXFmby+q6pq0WsVpyMTSU12VN1Lp1i+OEhfHalFtaZUtb3dIlJbrdZ9eufF2JrnI379+v71VwMK9t+3YABUDL64C9iJ+PqhF/+GHtfv/2W55rRIQezzTpBUlNZcjBthFIiwGmngSCe3PSZqYDXknACKcewAcP6nDD0087lj8BugHM8Y2A31zAls6uUcOXAyPG8bvwySe0xMPCgLfeYoncmTOcuAU6uWGvbwcWdKLrN6g1MPUUEPUMasTtC1wAYsfbFORub7D7VPPh1R8j9Qzd62vHswNYWD+W+oyaX/0GH3nJwM6fsmzo5Efc1uVV4KUbrCuubszWXsoGGUv7s6b48tfMzu71C4r5qHlASIfqX5uiIB04/gEwvwOwbDBXrAKYQf7kHop79zdrXv9cB4gQC98vjRszHvzttxSD9u1pdUyfzodVUhITt2w2WhDTplGsUlO5Nqx1xSSAMdZp02jFXbyoS5wUrVrp9YaXL3dcjWnIEFpDmZmOC0AMHMgHeGqqLp3x89PWzPr1FBgfHy3mqvVl+/YUzJQUZgl7eOiVgw4doqhZk7ZsNkf3dHAwXerZ2TpuDFCIbTbGQAGKcWUWsaoLLiio3DWtJiDOFrFzopbVIq6obKl1a97f27cpOE2acPJTWMh9g4O57+3bFHhVf628BSqR7uBBLuwetASIeY8u1u3bea5t29LzANB9f/gwr2/8eH2dJ07Qevb0ZFx46P9y2b1N09kmNScHaHwD6PC0Y7nJiRNa7CdNooVvpbSUyVvRGwHfOYCRA7Qax/rZrn14vRs38vv72mssb/LxoThnZOgyOYCCeegvdCMXpANtHmMiUIhTp6/KsJcCR/7OHtE393G5vid3A/d/UP04aX4a8O1r7Ll8fRvF8uHFLMcJ6131+9UYe34FzGwCHPsnt3V6gXXAIz4G/JtWb5ziPMa257Vjg4zEg0C9pnTxz0gCBv+1Fl2/TODmQXYf+7gBsOMt4PY51j0P+V9gRgozyMMHunSdaRFi4ftn2DBaUfHxelt0NC0x57693t4U6pYt+TCbM+fOsqXAQIqxjw+tsfXrHdtmqtrQ0lJmUqvsYJuNJU2+vnxYqnIa9WA3DLq0lRu2e3cK9O3bOqbZuzePr1pf2mxaUJRV3KsX/z5+nGKiXK3R0RQp5+xpZRVfuqQtsrg4nr/VPW0VYg8PXn9BAS3K6rimTVMLtbu7YzMPqxBnZ+se2L6+jolaaWmcyAQGcl/nbGnnJC11j/uUuf0OHuR1dejACUxuLrB7JeA7FwjvycXXU7PZqMXaC7ywUDfuGDVKx3CTkti0BeBnGxTEDk2BkcCFZUDGH4CQQsB2jJmvinPndJ3xhAm6UYeiuJhlTOc38NyMQqD9M2yGoVy2YWH0iKh4NUAX+aZNtOL/zwuRTnfr3l/z76H/5Dg1iUOmnqXFuPu/+HePn7KeNXxQ9d5fWkzr8PPmwKlPuK3v79lxqv1T1ROlggxg3+/LGmf8FTBL6cqefgkY+Xn149t5KcD+P3Ccba+yX3NoV04IXrjK8qiartZUmEVRX9gNWNoPODsfgAm0fYILUDx3Huj507vrdlaHiBAL3w1ZWXe6khVeXrQu162jMJw+rZcTVCJpxdOTbsK2bSkKc+Y4WrYAH+JTp1KQjh2jxW0V41GjaB1nZfGBqrKirfHizZt1XDg0VDfvWL2aD1SbTVvXO3dSkMtrfdmpE63aW7dYfhUURGGy2ylM/v68FrudE4fmzSlwt25xTGsZk6cnLS27neJbXgmTakNptYqr45pWDUl8ffX71DgVJWqZpuPSh9YmHoBjfDgri5MJd3f+nZJCK9bLi+GHggIdu1cu/U2zAM85QOhTQNSjfCCvW8fXhg3TC15s3szxW7bUE53CQmbJmyYndMpyPvZPPohNDwDdAfNT1qo2KvNUXL6su2o99JDj8ooAP/slS9h0wvcLwChlI4eHvnAsTSop4WQxIYGJfXY7J2Oq+xoAJJ2gOFxZx1jyY9uBZk9X3xorLQYOvsuks1uHgfrtgMkHaPVXt/722mZmZu94i2VA7Z6k9Trgj9UrySnMYsLUZ02Bg39iLPm+p5jMNWo+LfPqkH6RLTo/bQgc+COXSmzxINc+nnKcE4Kaln4lHWNS1ycNKOoppzghGPgXljU9soyhBBdav+UhQix8N+zezezoOXP4sHWu9+3YkQKwYgXduiEhFJTPPtMWlxV3d7YZ7NCB1tncuTrJShEWppv079vn2JzDZqObMiSEYmt1RUdG6oUerPHivn35EM3I0Bm8TZrQClar9Jgmhdfa+rI8q9iatGW3V+6eVslDV69SBKxxYqtF7OOj638LCyuuJa7INW2ND5tmxUJsjQ+npfH+BwczLGAtW0pJ4WcYEEDPgYoNd+rECYVyQffsqf8uLqb12agRcGopcOW3QMFYYNw7rPUtCmXWeHCw9pZcuKBbVY4bx8/bNGkJ377NUIaaHF3ZAOz6GX/PnwRM/pR1oOPX8n3x8fSSABR69TkpCgqAhQuB+K8B36Xc1uc3wP0fOraVzM1lUuHp05xoqJyF48d1SCN6DrCoO8tignsDgf8DLN7P45e38IkzyafYuGLfb/l3718y7t2kb+XvU9y+wM5TX40CbscCDbvRlT3my+pZr8W5rJOe1YwlRCV57Mw17QwwenH1Vy66eYCu57ltgVMzuS1qCuPjj20Cmo+omVAW55bd214stYr+nI0+Wo/neC9cAfr8suZtPL9HRIiF74YhQyi0kZGMZ86cCcyerUVZJW5lZjL7+dln+cAuKKDIqoe4FTc3uhu7dqXwzJt3p2hHRHA8gFaJdb1hb2++ppZGVO0UAVpkkZEUo9Wr+WC0xh6PHNFJWvffz2u7eJEx0PJaX3bpQkFKSKAVGBFBIcvM5HvateP5xMdTvKy9pz09dXzy6lXHOHGjsoeJWptYLZRw+3bNLGLnJRALCymKfn7cX1nZzhaxNT5cXAxc2w4Yt2nxWZO0AMcFHvLzdelOr148nnLhDh4MRM8Fts8A8icDvaaWeRSOAhfKsuVHj6bw5udrF/LDD9PbANALcuYMP9uJE3kNaeeAr8vqeAseAsb9jCId3JZWW1ISRdZuZ/xWWeWKvDyK663VgM+qsnP9O0tvrEKRnAzMmsXPMiQEePllJhGWlrL5i7c7sGEaG2sAQOkQwP1VoFVXenBGjapceEqLgH3/zZWckk8wjvz0EWDQX6qXyVyQwSSqee1oiXsHszPU00eq58ouzmdG96wIYM8vgaIsLpc45QRd6tVJnDLtXPN46UC61C+uYolXz5+xo9ZDC9g7uyaknGZ8+5MQ3tuko4wh9/8jE8TGraaFXdPlEr8LrHkr5fAfcIbCDxJ/f9bfRkfT3fezn9HqTE6m1Tt7Ni25l17iA97dnbWeqj539Wom6DhbCjYbraBevegKnD//ziYJbdrQ+gUYL46O1q8FB3M1HYDjK1eqahTi50eLS4lEcLBepWfNGoqXab2dPgAAIABJREFUt7fetmEDrVZr68v9+ykEyipWNclWq9jNTbtAT56kFezjQ9FLT3csY1LL7MXF8X1qJSPVpxm4M3O6qhixs0VsjQ8XFvKz8fbmOVktYmt8+OxuwGcxEFrmbrbGh+PjeU7Bwdz3+HEeu317iueRIzxOmzaA/TKw9UUg51HArSUF0TSBxGNAUQi9J6q+esMGWp9t2uie1YmJ2n09cSLj1flpbKpRWggUdQf6/D+6wxVpaRTZoiKOM3KkoxhmZ3Oil7YC8C6rXX5gFlswWrl0iSKcmcnJ0wsv8JpVOCXMA/i0PXBuAWB4AZ3+BbyxEZgyjROBtm15Tyoi6Rh7MR/8H/7d77+Z1NW4Z8XvUdhLgdOzWMerkqh6/pxx107Tq+7UVVLI7lWzW7DGueA2V1dSHoWGXas+h+J8nsO8+7jm8c19TAgb/HcmYA35O+AfXvU41vHOLgCW9OdCGKc+YdewyNHA+K9ZatXv99VPEPsusdvLLPXewL8rL0UTIRa+O6Ki+BDevFmvuTtuHMuWVFawFcOgJa1itrt3M0vVuROXYdAaGjCAX/aFCx1LkwC6sB95hL9/9ZXj6y1aAGPL2vytWKFbN9arpwV861YtOr168SGbna2zajt14jhZWY7r5AJ0iWdn8wFfrx7HiYvje3x82Pzi1q2KV2SKiXEsY/Lzo+Dm51N8rXFilaTknDldU9e01S1t7ahVUEDXvLc3Be7/6oebAvvfBOxBQIAXP8uUFL6/WTPHJC3nkqXiYp3sNngw0KAj4DkU8P4S6OwNeNqA2INACQC3IN0/PCaGkypPT35+hsHzW76crw8cyPtWWgx8PRHIjgNKmgMt/592Vav7s2ABJ01RUfyeWEVYJQVmLgW8ypZTHLMM6PwiHDhyhM1kSkrobnfuznVpLbCsD1AcBwR1AJ4/C4x8m9+B8+fp7XDuba0oKWAm8qKeLC1q2I1tJfv/oXp9neN3UcC3vsylDluN5VKHQ96rOimstJjiOSeS3avykoGI4cCkfex33bhX1cfPTwMO/AmY1ZTnkH4RCOlEy/fFOE5oatJRKy0W2PETxpM3TQMSDzDG3ve3jG9PWAe0eqR2TT3qkpIi4PiHwIKuwL89yiz1I4BZUunbRIiF75aHHqJr1iqEBw7Q9dizgll9x44sZ1JZ0PPn35nEZRh0+ykLeulSuiat9Oih43NLl1IAFd27M+ZomkzEUULUooWuI16xgg9rw+AEwt2doqnc0Spxa+9eilDjxrr15a5d3H/AAO6zezf/VolFhw5x/7AwXtvly45CHBJC6zQjg8JYUZy4JhZxZa7pijKmlTXcpAnPMz2dE4Mrc4GCIqCoP+Brc7SGi4u1F6JLF96vzEyed0QE3cj5+XRnN2sGxKcAqQMAWwBw4WfA5y2BzT8B7I35Gfv70wpW2dBjxuhe1F9/reuI1ee2423gxk7AHggEvgE8+rgW2txcinBmJq3sRx917C+dlgbM+RzIXwR47QNgUHzaPaH3sduZH6C6fI0axe/C/3keSoDdv2BNbmk+0HAMUPKKTmLKyeG1TJhAT4IzNw/wQX74r/x74Lus6a1OW8nMa+zOtXwoE5UaRAGPbaEFW79N5e+1lwBn5rMpyNaX2Ve66SDgiZ3A498CTftX/n6Anb22vUHB3P97ZohHjGCsduopxoKru0BESSFwbimwbCibjBz/N1eOaj6SrTZfugEM+FPNu4/VNUV57EQ2Lwp43xvY8SbvvWmn+z18CPDIykqHECEWvlu8vPjA+eYbPoCio+m6vXaNmccVxU6aNWOsrWFDxlk/++zOTGllQSuxXblSW2KK/v21i3jRIscErxEj6BrMyaFQK8t70CBa79nZOl4cGKiFd+1aCnRoqO4EpUqmnFtf9uzJCcWVK3TXqsnHyZMUBWvSVosWFMWEBAqF1Sq2xomVRewsxFXFiCtzTVeVMW11S4eZbAuYPRrwqQ/Yih3jwzExtBJbt+Z9s645XFqqk+iGDNGtLD2OA0gCGnQAIv8EFKYBvv10Yty6dRTv9u31Qg9HjvBY3t70othsTP459QlgugGYDjz1om7+UVDA70BqKr9fTz7puCZxcjIwZxZQvADwPAa4eXMN25YWq7WwkN8VFV546ila+f8n9LfYGOPIe/y7y7vAjf5AYird6mry0L27nlwpivMYy13aH0g/DzTuzUSoPr+uOnu4KIeL1M9uyX7VHvWA+z+i+LV4oPL32kuBc4uBee2Bzc8xmSysL7OXn9wFNBtS+fsBIPEw+zTPacVmHqadmdTPHAce31oWq61mAlb6JWDXf7Gd5YangBu72GSj1y9YGjVxM1tt1jSjui4pyGLJ1Zy2wId+7ER2+xwAE3D35WTh0U3A2wXAkzuBto9VOpwIsXD3FBRUnvUZEUE37LJltCRUf+Fduxinq6jMKSiIlrESxVmzGL91pn9/3Q967VrH/tEALSUVU16wQLvEVR1xo0YUHCW6hsHJQ716FEHlRu3alcKdl6eX4Rs8mFbktWucZAQFaSv422+ZjGO1igMCaPGbJuOmSlRiYviQV/HCmBjHOLF6aMfFOVrEyjWdmsrzBRwt4vx8oCgFsCVV7Jr28anYIrYmasXFASgBsmcBzV8FzCCgSUsgN40iVq8eBc6apHXrFu+Njw+v9cQJTnwiIji5OHkSSIkHvHfyPb3+BBxOBPKfBsa/y88oOpp1vj4+/JwNg+EE9RlMnMjzvr6D5TAAUPAE8PRPtZeguJgCmpjIz/upp7RAAxxvzkzAnAd4nAG8gtjUwprMpFzWFy9ywvLSS/w+KG7sAb7ozBaTAS2A1h8De4v4uXbsyGz9hQt5/UOcxO3GbjbVULHc/n/m8atKhDLtQMxCCuChd7mt2xt0/3Z7rXJXrWnnEoJfdAQ2PMM2j4160AMweX/V2cumHbi8Dlg2hNncF1ZwQYceP+HxRy8GGnWr/PwVpcWcQKx4gBb50b/Tpd5sKBd0eDmRDT2qWxr1XZCXygnC5y2AjwNZcpVRVr7n4Q9EjmWHrrdyOVlo+WC1hxYhFu6eRYuAv/+drtwjRygKzsI8dCitozFjGK976SW9KMMnnziuumTFy4sPTWVNLVnCJhDO4/fsqftEb9jgWLqkYspqhacvvtAtHL28mLylFoHYsYPb/fy4cARAQY2L4ziPPML3nDmjM5xVnG/TJorbwIGOrS9Vb+2LF/nAV60YDx/mduWSjo527D2tak+vXKHI1atHMSgq4r0rLOSkwN+fv6uHZmamdnkWFADnPwZ8lgIlxRW7pqtTunT9OuC5EwhuA2SVlao0bwtklU1soqJ4fteu8fj33aet4V69eH7qcxk8WLey9NwDIJdN/M+WnWO3bhT1rCydiDV2LD8Xa1x48GBOWDIuA6vL4v6Fw4EJv9FdyEpLuX9cHCcuU6bozmMAr2vep4BtLuB+EfALY22udaWd+Hh6ZZKTWZr10ks6g900gaP/YNvE/BQg4iHAfBs4kcxrHjuWE74nnuDfjz6qvRRFOXTlLhsCZF4BfNoDHr8FthYDeZaFTMrj5kEu5bhxKuO4zUfSgr7/A8AnuOL3mSYzmBd24xKCt2OZsTxuDTOpWz5UuQCXFDAJaX4HYM0jnET4NgQG/RWYkcwGJQERFb/fSuY1YO9v2Mzjm8eB69+yeUePn3Cxiid2cEGHmvTdrktybgLb3wQ+C2df6qN/p8cA4GSt7UTeszezgAlr2aGrFogQC3fPsGF8qDZqRLfqwoWsIV61ihZQRgYfPBMnatFp0gR45RVaCgUFrKXcssWxV7TCZqPYPfww/960ia5g5327dHEUT2vWtWGwFKldO1okCxZoKzAoSJc87d6tlzGMiNBrD69YQVeyygYHtLv9vvvoRs7L4zGtrS+3bKFYqxrYPXvYLatpUx7/3DmdtHXiBMXXy4vWk2oNabdTLKxx4vIae6jWkoC+NwV5wK1vAdiBwpiqs6b9/XXpUkAAvQdubhTA5CN02Y78jJMDAGjRHsgvm9RERWlruHNnnr/6u2dP3tfMTF57q1ZlrSzjAa+yDPWWb3AC4uXFxDdVG1xUxElU+/bctnYtv1MtWnCCV5gFrHwYKMkBijsD/X+rJzR2Oz0dyoqdOlV7DgBex/yPAY85gHscENgKeOoA0MDSWevMGVrC+fkc99lndRigMBP4ZqKuVW77E+BCP+BmOuP8M2bQDW0Yek3jkBDe+33zgZnKlWsAAVOAzjMBM4QTT+t5WslO4Lq+S/uxqUdQK2D8N4zDVmZBmybrqhf3YgZzymkguD0wZjlLkVqPq1yAC9KBQ39mHfGWFyjgDaKAB+cBL14Hev8C8A6q+P0Kewlw6Wtg1cN0pR/6M5CfCjQZwAUvlJhbP4Pvk4yrwJYXgU8bs2nJiQ+BnLKQlncDoP0UTnheT2f5VnUy2KtAhFi4e1q1ovs3JoZx1Lff5oINLVrwQTdzpnbvWvHyoqWgspv372fJiHM/aUXv3qzPdHdnDHbJEsflDwGKgVVUt2zRYqwmAy1a0CJeuFA372jWjJYKwAmEar85YABFNieH202Tk4eoKB5bWWsPP8yH2OHDtHpV68sbN2gZ9+lDN/W5c4x1W0uZWrXiQ/fWLQqf1T1tbXdpjRNXlbClrqvgEuAZxKSq/N1VZ02rjlv+/tprEBZWllluAO7BwMIugNtOoNENIPMmUJrHuurwcC283boxKUvdr3r1dHb54MGctOzeDXiVrVzV5VVgd1lC38iRHO/ECZ01riZhhw7xHvr68rsDE/hmEpB5AShtCrT6pZ4EmSa9I2fO8BqnTdN1xwDDHAs/ArznAm6JQEhnuoNV8o9pMo9h5Up93hMn8nMEgJRoZiZfXMXa3GZ/Bo4FAMVlFv1LL925chMAxF8C/j0QOPgcUJwMNOwHPH8eeHEBreDgYJ2Bb6U4nx2tPm/OdX3dvNgv+dkYoNWYikXUNIFrWxl7Xj2aJVFBrdlCclo00O7xymttM68B299iAtbe31A0mw1jj+1pZ4COz1bPYs2+Aez/I+uR144Drm7kYg5dX+d5TN7LBS+qu8pTXZJ6lu75j0OYLR49G8gry0nxbQR0ehGYfgV4LRV4eEHtFp2ohLsWYsMwmhmGscMwjHOGYZw1DOOtujgx4R6jb19axKrZQnAwLYGRI/lwV25WZwyD2c0zZuiuVx9/zIdtebRuzQdcYCAzjWfP1uU2irZt+dC12ZihrVppAnyITp5Mizw5mZa4Wu+4c2fd1GHJEk4IVLzY35/H27NHZ0yrhv6nT9NVrLpzrV/PY6uSma1beVzlkt6zh5aVnx8FPzHRMWnLmj1dUZy4PIvYmrCVk0Oxcj8PhI0ASjoBhSe4jivgKMQeHtzfzU0vN1lefNgeDnRbAgQ9CHhtB+xbga3PAHDnOcfFUdAbNaIAWUuWzpyhsDduzM9n927AvAx4xDCxCCP5eng4vzcZGToGPH4873VCgi4fmziR17rnV0DcRsBeDwh6G5hgyZDeto0TNg8Pfh9U8xOAYYWlH7FvtFsqVxt6cqfuvlRSwomXWolpwgRONtXYMQvZYCPjMtCwD2D8HIgp5D189FFm2Vtj0Iqrm4D1gwGPY4DhzkXnn9lLd/+pU/w+qcQzhWkC51ewIce+37Gnc6cXgZeus19yZVnI8bvo9v5qJBdRCGhOC/a5c2whWVktcdIxYN1kWq0nPqAl224SXbFPbAciH646ActeSsFdM56W9IE/cEGPxr25JOWrKcDwD2u22EVdceso3eEf1Wec/NxioKAsLFOvKWPtLycAM24BI2cBQRU8w+qAurCISwD81DTN9gD6AnjNMIyoOhhXuJdQ8dP0dEfr98QJWiMVudkUjRpRYLt1o5t72TI+iFVPaCsNG3JftSrTZ5/p+lZFy5a0ylXv6TVrtBh7edGyVusdW3tPDxtGUcnPpxgXFlLQlMt7+3bWf/r56VrkdesoQAMGcAKSkKATscLCOFE4fpzdm9zctCippLVDh8rc0wXAqa0UXE9PirSPD4+VmsptHh60qJVlV5FFrDKn3c8DjYYDph/g3hZIK4uBW2PEykoODHSsIa6okUdqmcD2+xvg+S6QO4MTC2uSVmwsxb1pU056rNZwejpw6CDgVba2c7dfAnvLst2tmeklJRTlNm34eai48NChrOs+u4AxO9MAbC8AT72is6D37uU/w+BnrSYuAM/zq4+4gpItE2j+ADN71fJ3ql1ldDTv4fPP6+YrJQVc7H7jVCYrRUwBro0Ckgt4n1591bFxiKIgnSsArXqIQuTTFaj3DtD5ZVqjCQn03kya5Bi/Tj7JUqR1TwDZ8UD4YGYij5zFuGxFJOznyk7LhwIJeygsD8wCnr9IC7aiJC7TpHAuv581zOe/BAw3oNubbAQyZmn1XLG5t+hynh1JF/TltUzk6vwyz//pQ0Cn56vX27ouubGXbT4/8KeL/sJKJoUBTLDr9V9ckenlG4y113S1p1py10JsmmaiaZrHy37PBnAOwH9AWxPhe0f1gz50iG6/U6coXGlpXCD9yJHKs6s9PWlJqGSWw4dp8TqvtgRQnKZN0wlY8+bd2RazWTM+RL29abWuWKEF19eX8brAQLrPV66kUCsLWFnMX33F7c2a6TKpFSsoMu3b86FbXMySFDc3LSRbttD9qlyM27fzdeWS3rOHngBAL9kXEgO4fwpE79Du6djY/8/ee4dXVafr359dk+z0hCSk0HvvQXoTAakqiCj2OjozOqNOcWbOOVPOzDmjjjrF3lHRGRvYQEU60qWFEkIJkEBCes+uvz/utVw7BcQy58x73jzXxRWSvfZqe+3v/dz30yx5+uhRS56uqJBzE54hHc6Iq6vBXQm2eogx9uW4CEo+Mv4fxojNsq1zZUynpFhA7PZD6JjKg7LGC6yj4uUcmXXcAwc2LVk6cECOREqKrmvVKnDukRyc0B2OZ1rbpqfrOTl2TOczbZqemXfftbpXjR9vjLa7Xu/zzofFP7Ocve3blSMAClOY9wy07+UGE7bXqQxm3nsWILTWrtJUIiqPw+tjNeze7ob2P4GcrhBATtUtt1hOUbjlLYfne2nwhCMSnFdD8RworNdzV10tx3P2bEvKrivW8IIlQ5QMFZOlWO6Va86fiXxmmzqKvT5Gs449qSpjuvmIGpKcq+Qn4FUN8UsDBJwnVyseOvY/FbOd/BjEdz73cUGOSf4qscwn0yVjV5/Q4I6Ln4S7SmHqkxeeSf1d2bGV8OY0eMyj+cZH31c9MkBCD3Uru6sSbj0G4//7f2Ui03caI7bZbJ2BIcCWVl67zWazbbfZbNvPNu+o1Gb/dywuTuxx2TKB0fXXi+35/ZJsn3++ZUet5jZwoKRqcwj9449bCVThdiFtMdPTBcbR0QKE119vCjzXX2+NQVy+XO91ucRMYmLkUJiL+qhRSvaqq7MAesYMa/jBzp2K9/brJ7n7k08EHN27i9Ft2qSkLZtNToPPZzGtHTsgsxOEImHjLdDDaGuZk9O6PB0eJzYBtaSkKRCTA/6e4DeT2vpAfb56QzscVhzZnMIUnjGdkGABcSCg+5KVBXuMeKlnMOQaCVtm7XAopMS1igoBWXS0XjPZ8LhxYn45X0CkcU+73g1HjmvbSZN0fFN+njdP6sXnn6spSHS0Pu+aAnjLiBk3jocrfmtlMO/d27TdpenEgJSaFX8Bzwtg80K/G9Qxy4xvhrer7NZNwGpOezr6oUCqaAfE9wLHT+FwlJ6VK69UDNvZjGXWlcAH1ygeWn8WokdA5fegvAdkZGr/RUVyNocN070LeJWB/XRHDS+wOdS04qZcI5Z7Dim4eJeyxl/NhuMrFLOe+AjcclxlTOeK4TZUWIMcVt4IpTma6DT1GbHCkQ+cPwPbvM5tD2mIw5sXi2Xa7ND/JjUiuXYnDLr9648y/KYWDELuW2oE8mgkvD0d8j8Gfz1gU4LZuP+GH9TCzbnqVhb5NUZQfhPzN5735e8MiG02WwzwFnBPKBRqURgaCoWeDoVCw0Oh0PCUlJTv6rBt9q9oHTrIu582TRLx3LkCvMRELdB/+5tib63Jzqa1a6eFasQIAcHbbwvczXiuaa21xfzHP5q2xUxNVT1yXJwW21dftcAnKUnn5nZLslyxQoASFyc2ZbcLQHfutDKv4+LE2Natk4w4d6729eGHkl2nTbO6cOXnW5nXGzZo36YkvWGDxZC3boX2HSDQC+ozYd/PwOUQ4JrflyNHJPVC0zhxcbGuI7w5SlUV+HdDMAXK9gJ1EMiDqG7gMpSDxkadZ12dfg9nxKBzNTPhQU7AcUNO7jStaTet8CQtkw1nZ+uci4p0fv36yTlxbwJbDWROgJ2GEzF9uj4DM4SQnS0n5uRJOXSg9qMRNnhrJnjLwdcbxv/OGneYmysHCfT89e9vXcfq1bD6L+BZArYgDL0bpj1nSbRbtzZtV3n11VIaggHN3H1nplhU2gwouALK7Pos7rzTiumHW+6b8EJPOPgaODwQugrOzACb0bLzllvk2FxxhY43bhwceQ9e7KsM7IAx7/jWfLVxdEW1PAYoyWj5fGO04nvgjhPI3HYCht1z7vdVnVD/6CfTNMihrlgKx7zlcON+GHjL+ZOmQiEx9Q+uVlnPuvsVL0/up8lUd5bq/qZn/8+MHAwGjR7Uo9Td6r35agQSaJRTkDJY53V3A9yQA9k/AfcFjo38JhYKKZlv+5807erP5z/Wd9KY02azuRAIvxoKhd7+LvbZZv+CZo7+i4qyEnKSkpomlpjWfLB6ly5atNatkyy7Zo2kzDlzWnYYMs3plNTbpYtVCnXqlBbk5tmo/fuLxb36qgCislKs1mSISUkC4xdfVJ3rkiXqDWxey3XXSd7eskV/mzhR8vT8+YpNLl+ufXTuLAb07LO6ho4dxbqGDhVYL1smYJ8yRT22P/hA8uagQWLBa9ZIWt2yRSx4/Hjt48QJKAtAUiwUXgTVH0LqdigYItDNytK1m/HcEycsadtM2CorsxyQ6mpwJalj1a7PIaYW/O0glClwNvcTFWVlTMfEWKVLJlsOn7iUkQ57doAN6HYpbPtEYOXxCKyjo3UvlxrjAocOtf4/bpycoBN7IcaYehW1EKqL9Pn27y+H5+RJOWwXXywHwYwLT54siXnZfDkWgTTo9e8wxqjbzM+3jjV1qnVvQiGB/9YnIOpd/W3Uf2gwgM2mBXzFCiuxbPp0OUc2mwbWf3gN5BsjMJNuhbx0wCZlY8oUqx7YtNoi+Oz7AmKAyBFQMh5CMVI2Zs1qmrmdng7ucsWO8w2Ho302THoM0kda7U+LiuRwTZig+1N2SA0lDhrX7PTAyJ/LwTgf8yzeBdsfUmKSaT3nawpS+shzv8+0hnLY/7I6mJUdtP7eZzEMugMyRv/PzfoN+lXPvOcZOLtLSWym2Zzqzz3oduh3/f9MD+raM5D/qT7H4yvl3Fygfeuzs9lsNuA54EAoFPrTt91fm/0LWzCoxeD0aQFScbEWinbtLGBOSxMjbi1j1OXS4tWvn+pDCwokVQ8fboyLO4cH3revFqw339R7nnhCjGfIkKZf+qwsgd5rr2m7p58W2JoSbny8ZOqXXxaovfSS4sTR0XrvNdfotTVrdC4XXaRjT54syXvpUu0/KwvG94Z1Rtz5zjvFco4cEchv3SpGt2uXFtAtW7SP3bsFvhddJKDYsUNy6ciRArvjpyAlGgod6gzlfBycNtjfWWB/6pQAp0MHAZZ57adPKxP58GGL6VdVwbD/0P7T90DxO8AEyFwMZ3ZYQBxeQ2x+xklJVvggLc3KHK7NE5O1p0GZzfpswvtKm8x40CBde2Gh7nv//vo8IlYBQeh+NXxhlIdceqmOZ858vuwyPSv/+IfOrVs3AfmmX8ORtyXfJ90LcxZYXbaWLBHojhtndTILheQI7X4coozY+KRHBVYgSf/NN+UgOBzKbzA7ZRVu1gjF2tPgSYfGRZAfq/t1+eVNO2qZxzq4FD69Q5npzliomwHVvSEySg5l//5Nn9f6MmURf/EX/R7RTrXUDIWPD0LxOuszqKlREtnATNj8V4EhqIRpxE/VAONcNbyhkJyJbQ+qYQaIJQ76nt73Vd2qQiFlXO95CnJesv6e2FPJV/2uh6hWYuP/DPM3wK7HFW8vyQHCVCC7Wwx88Peh54LWCcJ3ab56JcId/xhOfKK67HBL7qsmK52mSm2479wO0nfhJowBrgX22mw241vIA6FQ6MPvYN9t9q9kDodKf5Ys0WJ91VWSis+etTz2TZsUSzUXw9asfXux061bJTtu364Y7cyZ5x4Jl5goEF21SsdYvlzy8KxZTRvnm20x33xTwPTMM2KwpnwZG6ts6iVLBGAvvCA2HBcnKfSqqxRHXrFC+x0yRIt7SYni1K+9JlnxxH9CQjFUz5Acet11kq1feknv7d5d1/P88zrn/v11TzZu1O/TpgmIt20Tu4qLg/IaSG7UtZaWw7xn4NPL4USy1RAkL0/7PnlSrN/tbjqLuLJSLLe+3opZhoyfQZ8lX5vMObyG2AwVhCdqud0C95QUtTMESB5j9Zbu1csqWRswQPcV5IiYsd5x4wTWpbsgeo/Ao2QEUKHXkpLUMAN0nR07SrY/fFgs/fLLFfPb/GvjObwVrr5Lz+PZs3Ke/H6FMczBD8GgZO6Df4VII1N82gvKGAaFEF57Te+Pi5MTlpYm0Pnir2rcD5A4Ck6MBTxi5FdcYWWmm1ZTqNaaR5Yb9ywbysYrU33QIH3WnjBpMuiH3U/Bhp9b5WT974HPoyBrIKQlQ+8+Op/oaH3m774APY/DOz/V9nanRhoOv+/cMdyAFw69IQZsgkRkIgz9EQy+86vBs7FK9cp7nmoKMr0WCoA7TPyfYb/eGtj5GOx/RT24CcsBcUSKhQ+7WxOm/pkWCkLxbjk1+R/DiVVNX49Mgs7TBbydpn6tUYzfGohDodAGJFZI0El+AAAgAElEQVS12f8fLCJCi9ZLL4kpTZokhpiVpQV9zx4rNnc+s9vFDHv3VnJNXp4yR/v0EUOKbcV7dDiUudy5s8Bv716xxCuvbFqeYratXLlSbHTpUi2GZnN+j0fy8auvCtCef17dkhISdD6XXabEr2XLBFR9+khCLyvT8f7xD+g+T8AUWAanc2BVCkydKXa7ZYvef9NNAvIvvtC5zJplOR2jR6vMZ9cubZ+dDau3Q2mR/r56NeTXQfwlEPo7lN0igC0qsmLMZoet/HwLYM3M6fp6C1hDBjMIeS0mbL4WGWmVLJnx96Qka3iGmQjWsSPkPar/d5gKawt0n/1+SciZmXLE6uq0rderexsTI9b8+N+scqXOt8KuCjHl8eMFuoWFUlYmT9Z1mQlyCxZATS68f5V+910GN/9Kn2FFhZ7DhgY5AWZTlUBAjtjRxyDic71vzlvKkAad12uv6R5lZupZiYnRgv/xrSrZAYhdACf6AEYewoQJLet7c16CVXeBvw6ccVA9HaqNmcuzZ1tzlE3L/xRW3w2lRny953wY/0eVzpx4Vs5gePnTgc3w/o/AvhmOoHMZ9mPFOM9VvtRYpTGGO/4kRg+avDT8PnWFOlfc2LSiHZKec16U0wA6v0F3QP8bz1829V1ZQ4UY/KHX1foz3FzRkDleNdSdprT+/u/Kqgss4D2+UjOZw63jxQLdzpeoTWh4Y5SAV7XKJ1er//h57H95eGOb/X/SoqIk6b7wgiREcwLRwYNGG72jYgIXIg0lJAjY9+2TjHjggEB52jTJt6153D17wl13CYzz81VHPGOGAMrc3myL2a6d9rtypVjtpZcK0CMjdQ1Ll4pZP/ec1fRh0CAt7h99JOfg2mu1oF51leTVI0dUl9lQDJevhzeuhV2LIebPMGWhmNypU2LuF1+smHVOjkB54kSdy8cfi0GbQPy978EaF9SUQ7IPnLsh9wmISwDvODiUKya8d68Fjvn5Au38fAtEy8oEpMXFFugGjc8h2AoQR0SIRUPTBh9er/Zj1hLHR0AwT6Du7AmcaSpLDx7ctGTJzJQeO1bOR8NWiDqpMpxDaYBfn0VJidXf+7LLxL7NuPCUKdAuEl6cDgTAexEs+KPYeU2NQLimRs/DvHn67H0+eON1OPkIuL9Q1vHlH1kTiPbutRK6+vXT+1wuKD0gKbrsILjiwHcVFKYL8OfPF0CGW9VJ+OQ2ZSgDOLKhfCIQJeVj4kSrAxcYE4XutVhzyiDFgc3JRidP6rtjOrL1xbDql3D4OSuldsgPIPvnEBPmdIZb9SnY+WfY9RdJuCC2OPx+6D7n/N2zvDWS1vc8JSA2rcflYr+dLj7/+78LqytWBnfuP1QzHW7uOM1EHvFTyLiAWPY3NV+tmqDkfywANh0m01IGQkcDeDPHNXVqAj4o2moB74lVTePW57E2IG6zb2bR0VaCk9stRrxihZjZsmUCoSlTJF1+lXxls4nRdOsmgNq1Syx5716xivCOSKaZpUdr1mjR/+gjAercuU0bIowYIan39dclBZeXi2VFRem8r7lGC39ursD4hhskCY4cKWBavVrM+cYbFZu95hqB8e4z0D4WHGdh8lOw8jHY+AMoXwOz7oOX3xCr69lTLP6995RVfdtt6rF86pTAcsAAXeeePdBzIJxYAp8tgmg/BCugyy+huELXNn26ti0oUDy+uNiS5auq5HyUlek8wZKfA60AsQncDodAOTraai1qbtO+vdUopdwA2aiBkHtM/+/cWczfbpdDVViozyU6Wufr8Uhh+OsjEGHEf+MWwWm/notu3XQvQcw4I0P3uqZGMfGLRsBr4+Tw+LvDpIesUrAlS/RZdu6sz9Ph0DW9tgTO/Anc+5XANP8TzdENhTTty4x3T5ggsLTZ4ODr8NG1Yn/RfaHoEgjF6/zMKVymhUIqK/rsh8rIdSQoPBHoKXVizpym6kxjldpSbn9Qv0ckqFa1/83qalVcrPyDg0bik60Wln4AZ97gSwl20B0w8hcQm9XyewCSjbc/bMWNAbpfJgb8VTOEz+4R+933vK4H5GQOukPlR//shhZVJzR3Oe9di72bFpGo8Ykjfy4A/GdYMADFX1jA25y5elJ1Dp0ukTMS3T7svX6Nfzy5RuB7YpXCP+GWMVoSfodJcN+5x1G2AXGbfXMzwfCFF6wJR/HxAqCiIoFfVpZYYefOX70/j0cMZcAAAVd+Pvz1r5K/x45tmaFqt0vK7NxZUuTBgwKDBQssMAJIi4SrZ8CydWLrzz4rQE1KspqQvP22WOvzz8vByMwUODQ0qI51yRLFntPSJIUvXQqlHWHrk3DF65A/D3I6wNHPoWAGDP932J4voLr5ZmVUFxSINU6ZouN9+qnOde9eHWPxYjhwDPwZ0KcM8h6GQ69A7/t0biZ45uWJNRUXW38rKhJTLCqyHB8TiL+sEvO3ZMTm7+GlS2bCV0yMAD4uDk5/oL+ljoOck3JizCSv8K5a2dnWhKUxY+SQ2Teqg1XyMDgUpfObPl3AWFwswJ8wQdn0eXmS1ufNgxW3QMl2CCZDn9/ByNEG2L6m68zIkKzschmzhp+H0kfAladF/MrVkDpI1/ruu1bDkcsvl/wb8KpUyEyWipoKZ0YCDj2zY8Y0dSIrj2nYwYnPjD+MhIqJYIuCS6Yq9GGqQMGApN11P7HkzGH3wqhfQUS8nJ41a6z7FhGALifg9FI4Y3xuWVfA9Idab6QRCuk8tj9olZSBAHTYjyVFn8t89ZD7dwHw6c3W37vO0vs7Tz9/68tva+WH1XXr6Aeqrw63qBToOhNG/AySe/1zjl+Vr97b+Z9I0fCGV9vaDOA14rztwhLsggGpBSdWW8BrOi+mpY8U6HaYJBD21Sqh6+j75z2lNiBus29nCQkCrl27VK5it4u17NunpKRTp1Qy1L27ACj9HLJauHXrJul5zRolN61ebZU6hQOsaV27KnP5nXckGz/3nEpYzOYZW/8Ldv1NdauR3aHIKznb7LrkcCgJx+XSdZgJXB07is02NChm+tJLAtVevfT3T6rg+JNQXCjmXnAKquwQXQUjhinGe/q0gGnWLB1zzRr4/vd1H06f1v3p00eS/PHj0HmE2GTyVAGxdyukxkIOet18XzgTttkkIffqJYAyQdYEaROIbX7rNROkzdhydLT2a7dbyVsmSGdmwsntygTxDAOOiemaTVa6d9e9t9l0fp9+qvPr2hWefhii12q7+qmATc5Tba2AF8Q6T54UMwQ5JzmPQ+6rEHJD8k9g5nydzxtvWF2vFi/WcWprYcnTUPkIOE9CdIb6Ricawzpef133OTJSn3nHjpJx31sgILI5IXAlFPeQE7BgQdOSulBQmbprfiQW5Eg2WHA3XePs2VbjD9Bc4tX3QPFO4/mcBRMehqSeOtfVK6SKANi90K0Azv4dCgw5uf0s6HknjJjR8lkP+CTdbn9ITA4E7EPvUQLW+eK3pQckPe99VgABGmgw8DYYcMuFjy78JnZ2j76HrcVZo9Oh21zI/hnEd2r9/d/GGqvEWs1Yb3mzmeapQ604b8Zoq346GFC5V7jU7K9r+t72IwzgnajpUfVn9fkfekNlbOXnGO/azNqAuM2+vSUnWwMOwJKa+/aVHLxmjZiOyeQmT7YG2p/LXC6Baf/+ypA+fVoAm52tY4VnSoPY2+LFAr1Vq1QKc+yYFvmRD6hussMEcG2HhtehsQe8nAuzfwiDhwiA5s7Vcbdtk/NwzTVyCmbPFhgfOKAM3ZtvVmb42bNw8G147d/h2geg1xHIWQ8V34eqKB376ad1/b166dy3bpWMfvHFYtmffSZGfuCA2OOsWTrvvUchZjTUbIKC91QydPSo9nH6tMVaCwrEKE+fthQDE2zNbXxmlqnfAuAvZeuA9ZmBWLUZFzZjxs4SsFWBrR2c8Vvb7dkjBcQsdRoyRPcOxCY3bAD3ajkAKdPgaISeleHDpUqAPsvoaN1X0Gfu2wvrf2I8B7fCoh/o/N58U45WfLwcJY9HrPylv0HdY+A8A/HdNZAgroPY9iuvyLFISREIJyYqYeq9+RphGNEBymartrpXLz0D4RnO5Ydh5c1iNQCBkVA9CSLiYM6lYtbmvas6IQZ86A39ntRb5VKdp+mzWLtWYZRAAGiErgVQ/jacMUCx10LVOLc2/s9bLQDd/rA1ki++q+TnfteD6xwNI/yNcPgtAfCpddbfO09T7LfrrHO3vfy2VrgFtv23AKwJ6wRiO0CP+ertHNO+9fd/Uwv6lSRlAm/Bhqavx2SoIU3nSxR39hgNc0JBNeE4tUas98QqqxWmaWnDIGsidJwE6aPVwrNgvdqDrrxJtcTh5kmFrAmQORY49zykNiBus3+eORwCjsGDxQDWrROz3bdPsdvx41vPjg639HS49Va9/5NPBGQHDgiwejWTrmw2lcN06qTM5rw8tcdcsECZqXufhUWb1HThw99C/lvwybuQMwfmPQjRqZLXXS6B4pIlkj579RJjXrpUQPDyy4oZz5oFhW9D9Ufw8lsQ5QZbANwb4c00sfQJE7QAv/OOwGPfPp3XsGFiknl5At6ePRWnLi+XylBUBNlXwIFNcHo59HpI12227zx9WoBUWWkBsQmqJgCbTTl8IXCgczO3aQ7IJjP2eHTs2FgLYCuN+HDcCLFRl8sakdi/v5KxQOzwzTf1ekYGrFkK0TuV5HNygLaZOVPPQWmpmPaoUZKaa2t1D3olwstGCZJ/NtzwazHZZcus8YfXXy+5vKICXnwUfH8BRxm0GwwLVmrxO3xY7NnvlzO1YAFEuBWv3fgr7d+dDSWTgYimjTxAbGjnY8ac4RDY20HNTAh0FvhOmyYHAsQut/4RNv9Gv7uiYezvVacbsikcsWaN8Xn4oONJqF0GZw1w6nG5ADhlQMvnv6ZQCVhf/Nlo0Yjkz+H3K3P/XBJy+WFlTu99Rg4HqLxm4G2a3JTQtfX3fVs78ZnaXRass1i3afFdNb1p+L1f3Tbz61rFUSvOe3xl02PbnWFx3qlykGw2AW/pfuUImFJzc4chdYgV422fDRV5Yry7Hof3rmzJkBO6K4kr/SLlA1Tlw+nP9dydx9qAuM1aNzP72ePRguPxtOyle6Hmdgt0hw8XS9q0Scxp+3bFfseMOXczDxBbHT1aEu777wsMly5VbNLs9RxuHTsqC3nZMvUofvFFAaLTowVt2I9g4ROw9054589w+hV4ww3XPm4x8YgISeJLlyprtn9/MdclSwRGr7wiQFj4n/DiDqi9GDpmw6kfg3u72lS+maqM60OHxDI3b9aC//bbStxasEBAvH694s65udpm1Cgx5YpUIA44BW4DFM0pTKdPK6GpstICZxOATSZbV6cFxxuEKGjCiE3ZujkzNi0xUWVEERFQZXSdijSa9ffsacVbzfhsly7W6MqLLjJmDRudouIvh6po3UNzNKU5XGPDBj1ncXEwY7yG3Ye84B0KCx+VcrJypUIGbrfueVKSgPzFByH4ONirIX0MXPGBZNotW6Q6gBy+GTM0YeedK+CY0d4gMBtKh0BCou59RlhSUukBsRszfuodCY2TIT5F6ojZ+zsUUgvLtfdZTGjQnTD61wK9vXv1OVZW6t5nnoDG9y0npussGP2b1ocglOSI/ea8YP2t2xwBcPoo3fOSUn3G7drpOxDwacrR7ieb1rh2nCz2233e+UcmflM78j7sfBQKN1nOAgA2Nf3os1jtNt1fMYHt61hDBZz8zADej1uWOLUfYQFvxihddygEZQcEoqfW6B41lDd9X8pAK8abMkhZ9AXrVUplqiJNth8MWeMgub8czrKDug/hn9sFWBsQt1nrVloqsImI0GJbVycgNkHZ/DlmTOtZza2Zx6PY6siRYok7dwqEtmwRUGZnG6Uk+8EVqyzR8GSZxETJz3v2CMhycgReM2a07LLl8ajcaMsWZXOvXQsdpsPnv9OCFN9F8vnJCMjJhBPtFRtetEhscMIEncvHH4vl+Xw6xtVXC9hPnxZIL14M166WBL3vLAz7N8j9JUQth4I0WNNBgPPEEwKdm25Sctnx4wJos5b48GExtyNHxE4dDsjNgy7ToeTvUPwB2EeJPZvbmWYCsNkz2ozxVlXpPjSaX/NASyA232v+NGVtU+ZOjYOKQ/p/QyZgZGp7vVIeTPDt0UP3yuGQ/LzpOfAcBXcynOyhZ2fSJKvhxyWX6PzMLOb5l8EHi6D+FPg7wcV/E8Neu1bOid0uRSEtTZLzi78H+1Ngb5DMOPdtNXf48EOrXaVZ0la0A5ZdBjWnwJkElfMg2EGO3OzZlhMY9IvNbfi5frelQu1MCHSUczRpktUx7sw2+OxusR2QxDnxESX35ObCqr/rPPFD6nEIroQqo31o52kC6+YtJUMh9Ufe9qDlMABETwHnZCiIh9xN0PCZPgOHQzHwiQPBsV3st944hjtOzHfgbYpNf5cWDCpOveuvyhoOhvd/t+ke9LtBMevz9av+OhbwwektltwcnmQGmrPc6RLJzR0mi3GHQmoFuu95S2o25w2b1q6/FeNN6qOhF6fWq32oGYMPt8yxigXHZEGgQdscWW4l/DXZdhy0G6CWo95q4PFzXp4tdL6xdP8kGz58eGi7KWe12b+uHT6sbFOz41VDgxb72lr9/PBDsccBrUhqF2Jnz4oxmIt5TIwWu/23KdElMhnShkoeSjV+JnaX51lbK6ZkJgx17qxFtbUxdIWFKlGqqADPFmhfBddugMNvKwvWkwF1C6EkKBAOb4u5fbs1zefSS7Ww19Qou7qsTOxw4UKrfzXA4FNw5DkIxkPt7bDoJi3Kq1aJzc2fb5XtLF6skp1QSMloy5fLyenZUwli/VLhxF1q65j6Nzh6wpKxzR7ViYliWQ6HAK+xUfuordU9rd8HnpfA3wMct+n8Y2MVXzXl7aQkXY9ZFmX2ts6ogOrHwNkXyhdo/1lZul4z5p2QoL/t2yfAOnwQ6n8D9jJwXgPl3aUElJTofpodqp58Us/RtGlQ8QLsf0b3rO/TMPNKAbDZneu66wTMhYXw8m/A+TzYfNBjAcx8BXzBpu0qr7pKzHXP02o7CeDsAxUz1fFq9mwlF5rO29m9mj5k1tA2jgbvRA3imD3bGrZRUwgbHrBaPcZ3EQB3myOl5NNPjd7cAUg6Co7PoMFgyx0nw6hfQ9bYps9n0K/OYdsfgiJjXXTFwIA7YQMwfb6cXdP59XigrARe/QVE7Ybqbda+Mscq87nHFd8dCIIxVOEl2POkvptmow9QrXbKICV8Dbz1u+nrHApJXg9vphGeoeyMtOK8naZKEgZJxydXG5nNn7Xs95zcVzHeDhMF3qX7xXQL1rdMrHJGCqRTh8mxaSyDM1sVaw+/flDcuf1FVo139SltG1aSZbuPHaFQqNVhzm2MuM3ObT16CCiWLtVifdFFqr9NTlYc0es9d0vKC7GUFIFYQYEWsGPHVLaUNB3c+ZqFGpslr/PQG7D+p8q4TBksedksQ3nvPQHDX/6i5J/Ro5uWOmVkwB13aLucIJx5Fl6cDQ3b1THo7C5wPQQd74ITCCQXLlRsePhwMeN33pHj4fVKTr/uOiUc5ebqtcsvF1B/+CHszYIuo6FoE0S9DW/Fwh13igGfOqWe02PHiiGvXy/w2rRJr3fqpLItsxb6cAXE9ARfLgT2AvECWBBgut0CYRNQY2IExGYZTShktbjE3zKj2owjm/s0f5rsusHMzDXqODt2lJTsdFoduXr3tlirxwOVH0FkGXh6QFE3OTXJyQJVh0PA9s47Okbv3uDeIRAOOSDlZzBjvjUJC/RZdO0qgHvl38D9MthCqsWd+hRUVrVsV5kUq3nF+w3nyD8RqsdBu1SFBMyxiQGvsnk3/btxj9KgdjYEM5VQN2qUUWvdADsegU3/ZmROu2H0b9W3urRC35HcXCAIcXkQsRYaCsGHwHHMb7X4h5u3Rmxt+8NK+gGBw7B7YcBNijWf/bsl/YMW+JW/gpznwFYN1SjkMuBmyc/t+p3jy/YNzO+FvU9rsELJHsVUTbO7lLg06HuSnr+Lvs71ZWKt+R9LbjbviWnpoyzgbZ8twK88KtD9/NeKTzevRU7spcSqzPHKHSg7IMb72Q+grqjptp5U9YRO7KVM+uoTYt7HPmp5rmnDIamXPqPGaijLgbxW5h3FdRbTjkwEXjvnpbcx4jb7aqusFGvr3FnMxm5XjPeDDwQA2dmSbcOzTb+umTHpTz81ymgKIOYNGPsMZC+0tqsvg3dnq7XcGKP3sNereO7nhkyYliZ2abKY8GPs2AEfPgtRSyH2Npj/Y9j6E/XUBUi7GfIyAZvk01GjxJr277c6Po0fL+ZeUqJM7oYGAfbMmQLibdsg1gZRT0B9ETROgJRrdE5PPqnzWLRI96+qSgC+apUAdMoU/T8uTizo6FHoVARlT4K9H1Qt0PtNFtyunc7DZLQJCWL+MTFivh4PNByB6KfB3wG8t1rzhc3vvskKnU4BtfnThrqF2Sog4pdQ4rBkcZOVOxxyxvbtUwLawZ1g+73m/TbcCL6OAsbly8XAZ87Uea1dq2dnVm9YfqmO774DbntU1/yGkXk8b57k+6NHYekDEGn8fdi9MOFBOTavvqrPICvL6H9eCO9dASX7wBYJtZep4cbgwbrXprxctFMs2Oyj3DgOvOOhSw85C0mGvJn3jkYGVhnNTfrfJCfRa+QR7NkDBCEqF2I2QYPRFap9tgC409SmYZPaM+pnvfMxKys3bTiMuF+JWyGbauK3bpVT1r0bXJQA+561OnOBpO2Btyvb+lxZ01/X/A1KDtv/kmLlTfo6RygJacgP1DDk24JvwAuFn1tJVme2NX09oZsV5+0wSUMtKo+FNdBYrXBDuCX2MGp4x4jFlh0Q2z25pln8GrHojFHgaS/nquwgFG5smbAVEQ/tRwqoQyEd8/TmljXEjkg5J540ICSgL975ZZez8zHiNiBuswuzhgYBkcslKfHppwUGp8M80MGDBcrhiS9f10Ihgd6qVVC5HSLfguSfwfSbtd/iXfD6OLjtZMtpM4WFWvDN8puLLlKpVPNJUEVFupbSUr122WVQ/7FqPwFSLoGjwwGXwMVsi5mbK+Zl7nvaNF3/888LuMaO1fFeeUXAke6Fmj9o+7pFMOI6AeWKFQIhs7FHVJTi5mvWWM5DQYE1OjHRA74HlPXs+QMUNYhlmuMPS0stRmxKzh6PGGdEBPhOQfTjEEiHutt0j/1+LaQOh/4FAoqVNjRYIB5bD/wRSIDqH4LDyBGoqpJacviwVQMNuoZd/wHurRr/d/ZSyb/BoBhu165SK14xnJ6rpsJHl0CwDgLT4balcibMUqbp03Wfc3Ph7/cr7g4w5ncqSdu7V/cPlAg2dy4cf08zcgONYO8IVZeBLUmvDRqkbf2NsPm3sOU/9XswHepng7OT4sqDBws4i3fDmnusbksZY2DyYxDdS8loW7cCIXAfgvgt0HBc26UOURJW15lNAbj0IOx4WNn7pnWdqQSsrPG65+YgkNpaMV5PDti3AEbXMxzQ/RoY9SNIHdzaN+jrW0MV7HxEJX4VzeXZKDH6YT+CLq3UNX8dC4UEduHZzeESryu66dCEhK5yfsKBtzlLju8q4E2/SFKyyXhbS6xKHSIJ3R2nmO3Z3Vatd7gl9ZUT4PIo47xkX0vAB81ejs2SOtBQASV7wVvZyv56Q0wWtis/bQPiNvsOLBCQvLt/vyThmTMFGJ9/oub0oSj9y+iiRblfv2+eaR0IaPH+7FFgGdTdAL1Hg/ttOPoPeb7jH1RsLnyxCwTEjM2hAXFxYjc9mnUa8nrFXs3ORiNHQm8XfGDUl8b1geIZ4IuVLHjllQLMY8cUCw4GBdIzZyo2+OKLWmguvljs+JlnBJCdC6H0GQi5oPZ7sOB2JZDl5wukamoENEOHimlWVlqx1/h4gWRZGSR/Ct6N4J4HpYMs5hsOuI2Nciy8XuunywX+YjHbQCpU3arztNt13+x2iwGbQGzGl+N2QWgZ2EdD5VQpDUVFOq+6OiV+mcy4f384tB4i/6z7WfMDiMgQmL77rs7DHLRRXw9Tx8PeW6H2KPgGwqLlutYXXtBnOHGi/uXkwLv3QqTRPWryX2Cw0exlrdEoZMIEGDdGsdsdD+tvvuHQMA3SMiVFmwmFp7fAihu1YAM0TgTvWOg/SOcaE6M5xBt/pdpbUPxvwp+g0xxJ8OvXq7zJkQtJW6HByNht118A3H2e9UyGQqpj3fYgHH3Pev7636QynqQ+kty3bjUmWoXAcRTiD4AvrOdzMB0iJsKiP0LKOVpdfh2rL1ON76G/Q9Xxpq+5YiSjjzAchG9jdWetGb35HyvGHm6Z46xmGmnDJS2bDTROrhYDDre4zgLetKGSpksNxttaYlXGGLFeh1sli0VbW9b5Otw6blSKnILqk5Lhm1t0usDZGS0VoyKvpbQNyhmI6SD1wFul7YwEsTZG3GbfnYVCYkAdO1plQxv/TQzDGS/5J+QXINs8EJMKSVmQ3F1N7r9u6zyfD5Y/AEefA98gcB4ETyw0Gp571niY8JDKFcKtrExOwzHjizxggBZas/bTtF27xKKDQdUsTx8J627SF9sVA4HFUJkm5mm2xTx5UqzN55NDMm+eQPTVV7XPWbPE/p56ChoboPMWKF2pYfa+2+HqG8QKAwE5Ce+/b83SXb9eSoPbLdAza42Tq8D7iNo9Vn8PMEA0GNQ/E1yDQcv5MYE2VAkxf4JgEpQaQBwRoZ8OR9P3+f0CTZ8Pol8D+2EIXQ81nS32nZkpB8z8CWrecuxX4MwF20SomqBEvo0bBdqzZ0vCzc+HPr0h8Ayc/gwCmXDx25DZSTK/12upDbt2wUf3QITRiGLGEuixUGVp4e0qu7aD9xcajRtsUD8X/INUunTJJcb11Cu+u/0hvS+QAQ1zILq7zq1nT0mlu/4GG35hyJg2GPXvMORHsCtH4N/YAI48SNP6xLEAACAASURBVNwKjXnaV2IvZUH3WmANRggGJGlve1BJO6BY7tC7Je26k8Xot2412pLWgmsXxOwDnwEWNjv0u1GZz0VuxdPPV+b3VVZTqKEKh99uyfDc8eqlPOKnkD6i9fdfiPkboGCjxXqbA2RiLwt4O0wUMzVB9+RqqDjSdPvYDsqCTu6jpDBTam6RWBWlGHJMhu591XEro73J/jqJaTsiVdJ2dg/4m9U7251iuxGJeiZqTrYcQgHq4BabpWN7q3VOvuqW28V2ECO+5vM2IG6zf6IFvPDJ7Xqo5y6DE6WwbQ2czAVbPdjPQNQamLUFejQbjn6htuHXsOXXklYDaeDcB3HrwGeUa/S+Gsb9XskupoVCxmL+kcUSL71UEmX4OZSUqAFIUZGRTDQdCv9sxY2jroTi3hARabXFPH3aGsHXp4+ygA8eVOYu6PfYWDFlfJDxNlQfFPtLvFPnsGKFnJlBgwRY6ekCxKIiS/KNixOQ+X0Q+zhQAqE7oSbFYrCmtOz3WxOIgkEx+EAAnD6I/SME46DIAOKYGOM1p343xwfa7bpXjiAk/FFx4sqfKNZqs2nb2FgxeTNru1s39e71LAF7NFR+H7K6iznn5AjkUlOVnJaYCD0Pw/6/QTAGBjwH2Rcr8a2uTrLw3LmwbSus+qFkboC570L7KU3bVV5zDXAEls8X67C1g5r5YM9UuKGfkbhUsBFW3CB2AtA4BbyjYeQohRIiIuDoh2phabY/7L0Ixv4BjpYps7+6ChzHIGEzeA0QSOimRhy9F1kOpq8O9r0gZm6yudgOYr/9b4Jqr6TnHTvA5wVHvmY0h8IAq11/GHgH9F2s+OS3sYpjsPUPcOQ9qGvGBiOTVR6X/fNvnuQVCkm6DZebwy0ivqnc7HA3Bd7mgBqTAVmTVB0RCllZza0lVqUMUtMMX62YcVUz9gyqC45sp2EMVfktpW2QvG22Bq0tan0/kUlaWxyRAt2KPJUvNbe4Too5251ixOWHv9yujRG32T/fQiF527v+BvOWSTo6e1aLzp4/AmXQcBm0SxFTGTy4ZZvKr9q/txq8NkmS27cDfojcrjaKISMLeMRPFD8MX8BqagR6Jovq2lWsNbzNps+ncijzuRwyBNIPw/r79Xv0WDgzHnBZCUTFxQLj2lox14ULxfreMyTIq6/WsZcvB0cFxD0r77vhUtVYlpWJSffvr/h2WZlVVxwZaZSplFnx4PjtEPwAgsOgdpbFYMOZsd1uZUKbAB3lgNg/QNADp27Ra4mJkrJNSdvpFBCamc+OXIh+HQJdoO46gXp9vRyDqioBeW2tPpcOWVD6C3AU69p8I5TMtnq19j99ulgswOQ42HavEpLS/hPm3KkYe2WlnI8FC2DTethwN7h2K3t1/kqI6CfFwWxXuWgR5D0D63+m/fp7iwlndlN5WGKiFuj1D6iJC0AgSyy4XT8lzmVlKW679sdWZmzacLWlrEpSnkJJicAybhP4DZCO7SAA7nedVapTV2wlYJnJPqlDFP/tcQUcOabvQl4eUK9ri94LgTCptu+1AuCMUd/MWTWt9ABs+YNqkZvXzXpSFc4Z8TNI7PbN9l97xigr+gSOrWg5uKHDJIv1xmSq3McE37KDzc4nTcw4tpNGBpbmqJa6eWJVfDc5Po5I1UoXbWs56SiqnaRhR4Sk97JmIwxBgBrbAexuVWBUHmm5jdOj/TijlNlecbj1cYZxnSEqGbAZ+zrachuAuC7gScW2eEsbELfZ/5DlvqW6zUuehe5zJVW9OR0K1oItC+oHgW8AODyKi44YIbb0da20VEwlJwdsdeDZCPZNes0dp6zWgbc37aObmyuQrK7WQmeWp4Rnf+bkqLTG79eCP7Y9rL9ZcWNPdyieCaEEJWZNmaLM5RdfFEB07iyA2LZNMWqbTWMVDx5U3DrmJNie13Fqb4Jpt2k7n09JTJs2ibWnpUn+NhlndLQA3VYFsY+qzKfsHgg6BaA+n4Db59P7Gxokx9bUCCgT4iD2txqgkH+bzispScAbFWUNjoiO1nVHRID7Q4jYZrDHsRaomzHpcJm6eDlEvg/2DKi8GQYNUSlWQ4Mk5rVr9f8xHWCP4QhE3AKLH5REX1Ii52jRIlj3GWy7B1wH9Yws/AxqksSEAwE5PLMvhtV3qIsUQMNU8I2CUaP1mTocSuxZeZMR/7QZ24yEycZUJV+VSl52PqZ9RLVTzkH0eFj1mVi3/RTEboSgAR7R6ZKq+99odagqy4Udf7LiyaCkpuH3QfJIOVXbtkFFufYX+QU4wthvYi8YdDv0vf7btX0s2qkyrPxPJLmGW0ymspyzf3ruUYrnM1+dWOlxo6a3ZG/T15P7WcCb1FcgaQJv83m+USkKJ0VnqBFISQ4UNusFDdpPTAYQkizcfFADKP4bmSRFrvJoy2xngIQeSgIz47rNze6EuK7gigRvbevADALTiHjFkeuKWjofIKcxsbvWn6BfDkMYA29jxG3W0qpP6YEKeOVZBnz6GfRZf4vtAJljvv6+z2yHZfM0ESYqWXEyf51V/oEDvIOVUBNsLwDLzlYM7OuWRBQWirkcOQK2UohdByEj2SKhuxbX7nMthtHYKAA3h9i3by92FJ7pXV4uqbqwUO+bOhzyfql6Y2eMMnEDXcXgLr9cwPTii3pfVpYk040bJcU6nQLjdevkCCTvAO/7kmUb74JxM8QcPR6B2uHDVuctsBKnzGxoM25bPwf8QyQj2+0COp9PSVxmI4/ycgFxfDwk/E6VKMfv0n7btRMLNZkuaLv6eoON/xmcFVB6AwTTrCH3ZtwZtO+kaPD+B9jroe4a1Ru3b6+s8d695QycOgW928OZn0KgCkJT4PqlcngKC3XPrr0WPlsBe34MzqPgToSr1sLROqtdZXY2DG0P7883ZN9oqFsAzp4KBfTsKdVk3U/U5hHUpathDnQaakxJilfW8rqfWgt39s+g002wbosYq70QojcARkJXVApc9Cs1qzCbZBRs0gjCvHet56bf9QJgb5Jiv7t2AQ3g2gOePRAssLbtdZUAOGvCN2e/BRvV4/rk6paxybhO0PNKKUSeC+x8Z1ooqIxxU24Ob5cJkrQ7G800UoeJMZoJVs1BOjJJSVOeNAjUC3jP7mp5zHYDta2/Xqy5efaxK1oM1O6C+lLFbZtbdIbqdQNeycvNm26A9uH0CJhbk6nNbVzRyryvPtmyTMm8ruh0OWTeWuN4vpbbOaMkfbtjsV2zuQ2I26yZvTVDszhTBqsHrN2lfw7jZ2OFEiduO8fD+lVWdVL1vuWHYc6b+uLmf6IFMnzxCnWAhiHg7w8xiWLIw4a17B/9VXbsmNhlQYGkxJjVEDSAP3McTHy4aULXqVOSjIuNzjvNWxgGAtqfWZvcvxdELINco441OBNqh0FGppgcKIHr7FkB0eLFSu7Zvl3AtnixcbwiSHlPjTL8nSHuPoiNFwB06SIGHAjIMSgstOqFTebryIHot8DXAepvlGMRGSnAM7fx+ay6YqfBmlMeAbsfjtwB2KRClJbqtYgIAXm8MSc3sgZSn4dANNTdC34jlmxK4CZ4JyRA3ZsQsRGCPaF2kZLi9u7VNub0rcRoiHgWanMlIV/5AaxdJ2cjLU3Z1J8sh0P3g+MURGXAVWvg81xrmtOMGRC9XywXDICdDx36CoTj49UEYuVNmk4UskPjNGAUTDfKqE6uVomaCRbdL4PBv4RtRxW2sBeBZx3YDBYXkSAAHnSHSlmCAdXxbnvQSgRyRsKQH8LAOyG/Qud76pTA3LUd3LsBoxFGfFepNP1vOP+4wvPZ8U/UAKRgfesDB3ovgmH3QWTc19tv9SlLbj6+omUP5o4XC3jbj5TcfWqd7ufZ3U23i0hQfXNUOwFUyd6WLNMRqWxxZ6Qk3fJDLc8nJtNIlmponcm6YiC6vZzB2tMt74W5D6dHIYrawpavY9PoR0ekgLmmoJVtzHNJkINSX9I6GwaI7SiAtjvU5KMZOLcx4jZraXUl8OntAspLX205+WX7w/JML3nmmx/DW6Ph3+HZpADVBbDvOYHyl51w3AZLHgbBVC3o2dliSxfKGEIhycCrVkHJWXDmQPRqCJodoBZpKo45aD0QkBy8yvD44+PFjruFxc4OHVKtamOjQHFAOXxhNBJxjICKqXIgrrlG71+yRIlc5rzcVasETDExin++/rriV0kvga8IvKOgx4/FhBsbrfrc2FhJxqGQnAOzRzR+iHkY7I1QdCM0xChuW1urn6Wl1rVUVoppe72Q8SQ4GuHILRB0CABPn9a9TUsT2Hs8Ok7UDkhaB3X9wX+59m1K3yYzdjggohYijHKh2jshbaAcEb9f5WBbtgAh6LIRSlYpye7id+HgUakDiYmaYrXyTTj2c8WYY7vD5Svgo01SOZxOmD8X8h/TMwNG+8kpMH6iSpy8VbD2XnWpAvB3gYbZ0GeMADxwVoMZ8t7R6+0GwMjfQx5ylOxn1QnLmWM8irGQ/QAM+b6cVF+9Glxsf9gChZgMGPZj6HQl7DEchoYqcO2V/EzYot7jCgFwpylNvwcXYsGgJPidfzaaSIQnCNlUo9r3OjkD7q/R1MNbo1isOTTBLOcyLWWgmmlkjBYAFW4S8DbPgnbHQtoIMVFvter865u1lYxMEkhhE9g1f93mEIO3OaTStSYxx5j1uqWtv+5JNSTo2pZtLUESdHSGjtFYAY3lLbexOSTdOyLEzFvLlAY5CJ40seFAvZyY5jFt08w4st3dljXdZuewUEj9Y9feD11ugg7XQCCohfTQf2nQQPwYiMmG6KEweabVevG7sKBfSTK7n2za5N7fUYDs7wvpHcSSBwywQOAr92s0kFi9GqrLwbUFIteifoNIrsv+udUQpLTUapMJKkmaPt3qFFZZCW+9ZfQQBkalQO4DWhCcnaBinppGLFyojOpXX1WMNyFBkuvKlRbwTJsmMLafhuhngBDUL4D+V+ucXS6jTWSlxYbNciK/XwDo+kBgWZMN/kvEfEMhsWCztrixUSw3OVn76PQyuOrgyA3gcwp8z57V+9LTxb4dDsXF3UvAkw/F06G+hwDe69V+zYQwlwscr4FrP3iHK0nLHMjQvbuuv7ERehyHMy+pV/aAF6DGZTkmN94IK1+Hgl+BvRySBsH0N+GtFYobx8XB3LGw6Q4DAJxQfwW4hyohq2tXTf75+BYt4CEHNM6AiPEwew50yYAtv1fsFBS7G/U7KO8JmzYDJQJgl8GQnVF6LoberXnDdSVKPtz5qBV3TRmkrl4R2bD9Czl+9jNh7NeQQ2OyxKT732T1H75QCwbh4FLY/bi6TYVLnjY7RHWFuKmQOhsioi3Vw+UKU0BSmg5jCQbUvMIE3lNrmx7Tk6rs5syxug9nd0tqLmq2TruiIWWI4qWNFerN3Tx7ODpD4ONvhIpWYruRyXq/v65lXa/5ussjZ6E1wIxI1Hn468Som5sjQuEEECg3GUphmDteDgJBSd3N5w6bFttRxwr6oLZYuQWtWUymztvuEjjXnmlxbm2MuM3Obzs+gU9vVsJCh/vBGQHHbrUykU1LHQ19Fyjr8rueZ1p5XLG7PU9ZE2SIBO8Q8A4DV7oaZQwf3jTb+Xzm84mprF0L3nJwr7XKYdxx6tA06HZrRNoXXyge6fNJrr30UmvwezAoqXmdUdPaIxl8z0LpHpXs1FyhDONLLpG0/vrrkstjY5U9vWKFamjT0vT6hx+CczdEvWsAyJ2QPlhgn5wsIDLLikIhHd9mE7i6z4pR+z1Q+yMoN3pMV1UJMNu3l0QfCklRKCiAHm+CuxryrlFrRjNZy+uVw1Bfr+tOSTTKlkJQeR9U+cSuq6sVrzYzre0nIO5lJYDV3g0pnQXCHo/OpbgYOlZC+aO6X2m/hYTBllR/3XXwyStQ/Fuw10DaaBj1NPzjPatd5UVxsOpGLbiBNKi/EroMV1ze4YXVd1slZv7u0DALhl8MUyZD3huw7n7rWRr8Q3BOh41fSImIWKe6XdDnP+InYriRiVCep77Su5/gyxaPnabCoLuhrJ2eqZLTYtDuHZLTTes6WwDcedrXq5kP+sXo9zyt+GwofKiCU120Bt4u9vunR1XyFhVlOWjmz/JyPWdDhsCkwVaC1fGVzZikTeeYNUGya+UxjQY0a55Nc0ZJQXDFio22Ft+N7SCpuKG8ZYkUGEzULnk4vF+1ee8jkxXXbZ7hDdqvqUq01rXKGaXzD/rPLRlHpUoG99efe5vIZO2HkK6jNQcABPBRBuD66qG24NxsOCpF1+6OhlCojRH/nzFfreK2tUViAHVF8vjqiqy/+ergytVf3ws/dADevxccm6DrVMWKJz0qafng23D8Q7CFfYmS+wqQu85WTOjrNuo4l305U/UpOPGp9Xd/F4Ml94YevSVbd+9+YbJ1Q4Mk6A0bIHQWIlaBy5DiEroZCV1GN6TqaoHxfiNO2K2bSp0SE/X7kSOqFa6vh7go6PA5nDCzdy8B30UwbLgA+a23xISjohRHXrFCzLNDByVmbd4M0SvBvhkCyeC+H+qDAjtTWjZLlMwuWXV1AsSIxwXIpy+FygyrxMnlEhCWlOi9SUkC4t7vQWQl5C2E+kixTZtN4B0ZKYehrAwSi6H9e1DfHupvsuLMcXFW+0u/D+JfAkehspGZYEnn5tCKhFoI/An1YL4eui1SvN3plIz/2ctQ/gewNULWJdDzt7DMUEX69YHUnbD9j/rdN1iMe/I0ZasfeRc+vk0Ld8il1xIuVv2x/aQA2mRynadDyi2w9ZgWTfc6cBttDW12lRcNv08JTae3KP57+C3r2emzGLrdBHl1GtsZMtnvLsBwVKPbw4DbNH0orsMFPuhoqMLuxwXApTnNhiq4ldMw+C71kg5PkHv9dT2X2dnW9qEQfPE5rHoa0irBl9OyXWXqUJUWeVLloBSsbzlO0BGh77bTo65YrTHa2I6ScWsKWrJNV7TYpq+mdQk5sh0Cu1ZA1xEhB9lf3zpDdUUb8nN9640zbHaDCdugoaT1ZC27S9dvd0pKb41Rg0A5KllO0Jcy9TmwMjpDMXGHW/ejvqzVlphtjPj/iu14VE0HErrrS+pJ00PlSYPoNEktf58Ed5xp2Yf5QqyuDt75KxQ9DRN+B8Ou0t8LCuCZJ9TQIPkMBPaAt8R6X2QidJsrYO409bsbAF5+WAxh7zMqHwIIeTQ03jdUrHzECHn/FyKZ19RYPYId+RD5iYZLgCS5CQ9DurG4HTokubqmxsicnqqOT3a7/vb228oMJgT9yyD/r3pfYBDUzYQuRibvRx+pJCoiQjHiFSusch2nE3L3Q9yrEDoOvj4Q932xSfN7GQpZjTbq6/WehgbVT6dshOquUHeFzqm+XnJkVZW2McG2vBx6fgieMsi7AmqirJnSRUXad2ampOrUzdBuPxQPhbKhYvAVFXJEzOlOjl2Q8BEEEhQbjjQmPpktMO21EPscBMuB8TDwl8oit9k0lGH1c1DzCNj80HU+xN0K643SszEDofyvikeCYr0R42DBlZDigVXfh1xj+IavFzTOhIlzYGBH2PQLSbqggfRd74E9PijPB/d6cIcNFRj2I3WR8qRI3t7+kNWf2OGGwd+H2Eth3yk4dhic+8G1A5xhyYudp4v9dp154aP/vHXwxWOw/2XNym0yVCFSNcTD7tF3ybT6ejmAhw/rX12durBNmiDp+vAHsOdN8DZLeorJ1Jzk2A5y4s9s01CDcLM5FWd2RMiRbw4gdrccjUBj6y0dI42xo62y2Vj1J2+e+AUC8gijE19rjNIVY7WJbC0b2QRlf0PrgG+emzNS27R2fuZ+IpP1+fnqWmf0psVk6Zxtdm1bW/DlQIcW5ohQLXJEogHQPmxXb2oD4v8TFvBpAPWW30tSHfmAHiTTinbCPybDpD+r7Ci+6zcrjcjJEYAMGaI+vkuXKmHHHKZASHGx2BPgzoOGZlmNXWaIKXeb/c3qFpubv0Ft+fY8pWzNL//eXfHJYA8YMlygnH4BSkBZmeLHe/dIXoz8FGwG0Pe6Csb9QQldjY1KtjIHzWdkqATG7IC1YYNKoQA6NkLt48aikKkOT0ndxIQ3bFD81+lUx6ePPxao9egh0Cw+DDFPAXVimNGXCvxMSbyhQUBeXW0x16QIiP+Tjl3yAzhdpW1iY60krHbt9LnV1kKfT8FzFvLmQqVH28bF6Tz8fquvddpLEFkFJdfCWbcAuKFBzkByMtSWQ/pLkpPrr4RgP52jy6Vtgl5IegN8eRDoDgMfg83G/Zs3DzY8Cw1/U8euXjdA3XTYb6gTk7tCzk+04AfjoX4hdJ8gpnvyPfjkDsmToQhomAnpl8KlF8OxF2Hzb8QonVHQ+0dwPBPOHAX3BnBvsT77wXfpexOZpBGJ2x+2snY9aTDg+3L0du6H2nxJz66dYu6gRXvgbSpliu9yYc9vQ4WOc2hpyxaOrmhl9Q+/T8lcIOfrzBmBbl6elZsAYCuDpBKo3w0Rx5tmC9tdcoTju+penN3TskbXZldtrcOlpMnmEqwrxpi9W9EyE9nuMgYmVLZkmzaHHPDGKlpljm4DdFuL17pi9P7WpGcwmvPYzy0XOz1KGgv6zw24drdYq90hp+RcTNhmt7KtQ0GdU2vJX6ZFZ0hNcUQBQWVL15xqldG3MeL/a1ZTqCzQgo0w6RGVYdhsigO9Nd3aLqqdvuQZo/UvbZjivxd0jBoxwooK/bv3Xv392DEtDrm5WsRBjSacuRBfAI3NYkipQ+Tdd5staezbdAwCNQjY/ZTiyeZCEYyRbO0bCln9JNn17dt0JnFrduaMgPbwAXBthcg1fJnQNfx+Y8FOUOLR8uVijKCGEBMnCnzy81VzXFMDMV5IeBcqD4AtCmoXgLO3WOD+/Yot2u0aFLFqlZhNr15GYlMOeIypQzXXgq271bbS6bRGGpaV6bh2O8S8A/HHoTAbinpY7LWuTsw1IkJs2O+Hvusg5gwcmQml0bo3CQl6rbJS+2zvhvQXwBcBZ++EWiOGnJkplh4fr9hqwhbwdoCKq7SwuVySt72NkPAxBDarJ3aPv8AuA+SmT4etT4PvBf3e74dwop+k+qhIGFYPu3+j1/w9oX4eTJsHAzrDp3dKjgbw9QX/bJh2BcTkwbr7rEEC3a+F8mzIPwGujRCxmS9LhwbeBiN/oUV/9xOKAZuLdnJ/6HYjFGXAvhz1M3ftAGdYq8OOUxSj7T7XauZxPqsrhq0Pir03r1d1x6p/8oj7rTr9hgaxXvO7Zc6FpkGzuZNKIHAAGpqV2Ng6QscREBMrkG8xdchmOOR2qM5XLDbcIhLEButLaGHuWDkFrcrEMUrSak3+dcUYPedb6Ublijamf7VSboQdImKV5NVa+0gQw7TZzg+kkSbg1kh+bs0ckVJD7G6D7Z9p/VpAzl10hqH02YzM7HNkd5sWkyklwR2v+xv0Ylu4pg2I/2WtoUKxHKfn6/d7PbkGVt0lyWTyX1TCEZulB7lwY+vdaDJGq8A+YzRkjj5/PWMopJaN9fWSZZu/VlJiee1HzfZuXjVkiM4HWw4Ewr4I0e0NCXu2FiLXt8jA9tVpcsyeJxXb+/LvvdQoJKI/jBipxKi4r6ipzM9XzfDJQ8qi/TKhK9ZI6LpDdakbN4pJg0BszhxJzHV1mjCUmwv4oNNmKDOYcsM0dXSaM1f3a5MhwU6daiSRea2SJddGsfNQJNR9D3xGcpSZpBUZKdBMTpYTkVIKKcugLhHOLDJ685ZaMV2fT8ANMHArxBbAkWlwxqN9JiYKkGtrdR4dCyB9E5R0hpNjBMBFRSqfSkoSg+rymnIFam7VcaOirPpizzZwfKgErvb/BXmGozZhAux6CoJGDXb/n0JOqtSAdjGQvgGOG3H2xskQNVNSdOVnAmF/re5Jw2yVAg1vD1t/Ycms7cdAaA7klYL7c3BvApsBAv1uhFG/0v93PAK7HrcAImsSJF0OR5xQdEDg69qp5iQg9jfwNv1L7PHVz2T1KbWWzHu3Zd1qRKLqcEf8DNIG67MqKtJ35/BhPYMABMBRAHFnwH0c6pqVFcV2Uua2NwDlJ6C2WQMNcxtCrTesiEiU1NsCXG1WB6rm5jAGhLTGZp1RhjzbCo44PQK51gDZEWnIwefIVnZFG/0MqvjSmWpukUkGk65qvekG6DvsjhNAnysL2zRPe7Fvu0NraP3Z84Otpz1Ep0qCt9nlPDSUK/GtlWtuY8T/2+atUbyz4nDTn+WH5RlGt9d2N7dSuP5VFi5X+2vhluOKF4PKLwo3Wf9am9GZ0E3AnGmAc3Lfr1/rCAKMY8esOFaVIVHZC8CVC57j4A+ry7PZDfl6jmJs5jl/EyveJdl673NWPCkYb7DkIdAnWyy5U6dzM/JQSED66adQcrCVhK4/SnkoKZFSYMqFgwcrMSsqSslXK1fqutMOQZ0BPL6ByugdM1EgaY7vGztWwBwMGt20jkHk39XeMZAJVYsV46qsFLAWFwsQz5zRfmI80O4pcNdD4UI4afSbTjDyA2prrT7SvTdD/EnImwxn4qzBD2YDk6oq6LUJkk7DmYvhZLIYeFKSlIDkZIj/EGIOQeNAODtZMrhZUuU4DLHG9XrugSKj1/eIEXDwCeAD/d73V7DdkLE7R4D/eajME9DWL4Bes2DyUFj3Q6v/s28AOC6HqZOh6CWrXjimI8ReDbkhyc/ujWAzPv8+16gdZWOlErDMuDJA1yvAPglyyiCYo+QrZ5hknDlOzlePy61OWuey8iP8P/beO0qO+7rz/VR17pnpyYMJmMEMBjkDRCQYxCRRNMWoQMmyLFuyZUXvs70ry+vn9dk9u0/e1Xs+tmxLlGRlylSgJAZRoghGECBI5EDkMAAGg8Hk3Lnr/XF/1VWduwcDEhRxz+nTM9WVurrq9/197/3ee3n9f4qoMd2F6auHjrskJap2ofwWp09bz8j4uNwr2hC4zwj4hg+AYYuJOrzQuB68lTA1qAqJpI3Zs2z8EwAAIABJREFUZsehbDFcd2V2l6/DK8rsDBaoqfzYLMDm8OQGPDMWm/UznzDxbICs6dJaMB7MzUjdKi4bGc1UXZvmqZLjmKUlcwmrnH6bsComwJnLJQ6yrq/eCgHGgrL/bNfabpWdMqZ5KuW6JRJoDzxxDYjfUvvlfaIEbrlRxBhV86FmgbyXNUpnlP1fgwd/Pf1jTPSIGGPevbnXiUckH/PCNguY0wcPp19qwZrA3Li+dPGVYcjgbQ44Zn6uNiwubP8ZSKQJS5o2ClPuvEdq107HhR0ZV/mXX08tPBBdIiy5ep0UmlixInfDiURC8lyfew4mD4Hnt8JQQAm6viLXZPduEV7FYgLCd91lNW/4yU9UMY1u8DwqE6R4k8Q8F20UhbPJrNesETUuKLHTOfB/ExyDEFoDI6o70MiIMOJgUBh4Q4NUcJp9CBoOiGv61HJLoBUKiTsbBFA7X4Wac3DiRuirs1zePp9qmxiDZY+CnoBTfwhxjyXS8nik5d/8pyGhQ/+fQNgj52MY4B+H8m+J+Eq7HyZXC9AuXgznHgZdfdfO/wZm5GLhJFz8Rxmc460QfD/c9WHw7IPnv6DcnmXCgld+UARkr/93uYd1FzR8FE7UiQLavRU0xdYWfAA2/Z2UU935f6x8Wd0J7R+FsZXQdVaYr2u3CMtA7vvlnxTtRe2S/PdZ/yHpaNT1m0wXqb9RnsH1X5KqTdmeA6bE7V3eI+VKo2kpNXXLJeUmMg59uzMBzD9LrkM6u9OcqhhFWls/yA2iujs709Vd2UVSeT/LA+Ig1zgRy348ULFiLbc7GZQr3ZVbWW2ar16A2UgIq83HbD3VArhOL2BIRbCp3txpSSDAXDFHhKpO5WGKBwXYx85nBfdrjPittsle2PE/4eiPRI259i+lYIBpxx+DJ98vMdy6ZRKzqlOv8pbLj6vmMsOQovg92y1wTi9ZBxLbbb7eAudAW2nHsTOB48cVQITAeRJcJ4QxG7bZdGCO5cKefVNxMbn079W7U1jyoe+QnB0naiQn2bgOrrtJ2Jq96IHdYjHJeX3xBYjtBs8W0O2Crv8FWq2I2o4o5jx/vsR/vV6JKR8+LJOPuqekebzhE4HTrOslNmyCsdny0GwxOHUG/A+Le3Xo3RBZYdWP7u8XEL5wQZhorQEtP4CYE44+pHKSw4ptISDqdELHa1B/Fo5tgIFmWcf83OOBqgGYtwXGquHQLXJdEgnlPq6F5l+C9yJM3QTdi2TSMDoK1W7wf0u6S8XWQuR9UhRmThv0PwwO5eZv+ls47gBisOAoXFQpQpENUPYQ3LUZ9nwJzqsqZ9FV4PsQrKuBw1+2WgrW3Qndi4FD4NkKmrpv5t0nMeD+A6KANitF+eqh/gHoboUJlffrtIVsmjZK7HfhB6WIRC67uBN2fhnOPpc5yJa3woIHRYXtrkllvWNjiLv5vArZXIBoWpee8tkSUopHpCRkOsh5a5W6OF085RaQTgdqzZmah5xc7sjBSnMsl4OQ1TWsO3MzWN2pXLU5ANfpA7QccWJlZk5vOA9bNUVami5x23xg6w6IK9vhke8aGS/MassaFRsuV983Kr/9RG9+F7e5bcUcEXK5KsDhRrvr+9eA+Kqw0TOw/e9lJr3uv8DKz0ic9JlPWO62dHOVST1oE5hrl8q7v/7KnGN4TGKuPdslBtf9cuYMt7wZmm+QGHPzZolZ2bsc5bOssbEEOM7JAOk5Kbm+pjm9MFeJvTruKr1DTWhEij7s/7rkapoWXS4sue1mYckLFmRvOBEOS/7r1hdAfxU8LwjzA1G6bvgbONMLTz0lYKnr4qpet06Y7q9+BUSgZgtEVfpM6E7w3AqrVouiGqz823hc3MXaQfD9VOYQ3R+A8gUCvg0NoooGcUH39sKi56FyEM7eBBcbrPNwu61J3Nw90NgFR9dAf6uAbDQqv4fXC/OOQtMxuLgCTnfK8np1j+mHYP6rErM++SDUNwtbrq8B7w/Bcw6ibRD+mEwEGupg/JvgPAC4oPIvodsDrgmY9VsYPSjrhe6HJQ9JbPrlvxKXbKJCmjRcdytMPALnVaw9sByGN0O0S3KBdTWId9wlv8PF16QLklmwITAfvHfCGV3Ow7UbdDVQOzxS8WrFp6BhZe5759yL0tih+yUZ6O0W6IBFD0mVrclEmlbCAH0AHKfAf151b7KBmdMv4Q4QxXY6YJl5uOngmIvV5gXSjJXJ7rbNtbzA/vMxZ4db9puLIWsOmfzEo7nFWSCMVXfKOvnYsqtMANzhhnhMlN/Z8o2Tx9cltctdqVzVcfEmTPVldrBKN3+DTKC8NXJczSGTn8iEiADHz1+rrHXFbWpAXJ/9++TCb/q70gpaDLwB2/5WuhRt+jvY+b/h7h/Lgzb4hjTaHjgEg4cyG2eb5quTerB29ly7NJVpz4Ql4nIuJjBf2KZay9lM04W5mkKwpo3FA2Y2tag2AM5jwpYdZ1PXn32TVUikZkHx38Mw5NwPPGxVYwKI10ss2XsDrL9JXMVlZZnbT07C1q2w43lRDpspMa4KuOF/wMI/ghdetvoZt7SImMswRFU9OAC+18H5G/k8ulLY45oN1jZ1dcJ4o1EB0LIXwPOqxLtPvA8Cs0SMFY+Ly9jsDtXSA7O3wVA97LlOANheAMIwYO5BmH0Gji6HizaPRkKVNN38KpRPwJE7IDxLJiCRCDRUw9yfCYgOvVeUxW63uLQrtkDFAYhXwsQnQK+AgB+i/y6TKs0Pjs/AcBkEeqQkZmxSrnn4IbjtDjj7FehRKWmR66D2AzIhOK7U1e46iL4bgiMKgJU7cs4dsPLTMlHc968WGFSvhfAmGBhS7meb2KlhjcR+F304d7jl1NOw5x/lXk93TVYvkNjz8s/Bhf7U7AFtEhynhfV6uiCRNpBXzhXQGuvKBCZXeXY3a1Zmmwcwi7Zp7CMXyzY/g9yf624B0nwM2OmTuHVWIZnNHF4lqHLKBCZfPBgEmL01ioUjv2loqDDQemulKJIZe9Z0EXBFxmSyl6sOtd18deLdq2gFbw3and++BsTTMtN127dXBEF9e+UVnbBY6v6vwZ+HimeEdrv4GrzyN1LS7s8uZt9HdEqaL9jBeeBQ7huholViTCZzrlsmnU4uR6GcbhMXbSKwbamqZdNqFluu7ObNojot5GK350+eOCFpPUyB84QM7K7jJGv5ggyMnffIq3lT8UUVpgakiP/+h63qQwYQWyV5ycveKyy5pSVz25ERKXW5/7lUQVflXLj5/4BrjYi5zOYLN94oivNnnhEFuuMUlD8GiaAVN164QVzTmibx3MlJiQUnYlD7GLjPQagdzt0BwZAIqLq7xaXs9Upu75rHwZGAne+BsE/A2iyNaRjQeRTaz8DRRXBeidbMlzcE1z8vNahfuk1SYcz4b9Ve6DgMoVlw8GZobRMldss5qNwizHbwD8AzB9wG6N8D11nQKyH0cQgHoG4fhJ+U6xFdDuV/CMunYNffAwmZaETugSX1cP5hi30674QJXXKBTTY7+2ZY8gfSms8s3gFQ9S4YnAuxcyK+0tVAqzmkf/CKT0FjljEwkYDjP4N9/yLlHVNAUpPnaOkfQutD0NUt9+WpU0BMvDiOU+A5S0qTB1BNCMpVZ6A0QHf68scf3xSbDhjrqtBMju0cHonJ5mLIINcEI9PDYDfdbSmdYzmqaNnNvNaaQ8XOR/ILsEA1bmgQ4mKqwmNBcYWPn88dx06eo1MKK5U1K1bsl4kWhojWwmMSZ564kGxsc40RT9de/wfY+tdSeWbB+yUntmG1dNTQNMnbe2QDvP+3ssxbPb14bixcfH6vaeFRyam1A3T/gez5gCBAaGfPdcusxP7LtWhQSgqa4Nz9cuaM01udltO8tvDkwF5R6PhxCE6Ao0ux5eNWEQ6QB3fevcKU299TnGfAMKSC0/6HU1W18UZhyXXvhg03wdKlmQ0n+vpE0HXy2VRBV/NmuPEf4ETEUkfX1EghkNFRiR0bgxB4TPrTGl4B48bNVn1os7702Bi4QlD7fXBOQe8KiN0qIFxRYZ2HpsGSQ9DQBWcWwZm5qUAMMO8kzOuCo/PhbLssM4F49gVYfAgutcCR1VY5zVoPLHsc9Dgcezf4FqmqYAmoelQd/27wrgFtCnyPgPMiaHUw9mHQvFD7jCiBQUpRLrobJr8D/cpNH1kPs26AxFMwqmK3rnUwXi2VsHQVi2vaBPPugbNbrP64mgP8t8NAmbonbKGHuuXCfhf/vioIYbNEAo78APZ9TcRQ9lin5hBP05I/gvLb4ZTKBBgeAr1PgNd5OlVlDQKu3lpxS6aDrMOdJV46E8z2LbJ87mgQYDNBNJdpTssrEZnIzaZBWLC3yoqJRyYKA607IPFdd7nF5qNT8vvkykG2W0WrCO+81RbIGglxj4fHpKTw+Nncbne7OX0QmIP2x0evAfG0LDQitWD3/LO4W9f/NTTb8mknL8HXG63/nT4BvEC7VN0JtFt/V7ZnDghXwqb6xPWdZM9vCIvP5RZKF4fVLZPznU4Kk2mGIS71nm2WECy9zRpIjWozp7n5+vz1sQ1DYqMmW+4+LwOj85iwZUcaI5lzh1VIJDCn8DlP9oqwa9/XYUKlJhm6pD9pm2DtvdJwwkwNMu38eXj2Weh5Ok3Q9SFY/Jfw4gHF7BG396pVEk/u6wbfk+A8JJ+F7gTv7SKyMgwrb7i/H6rHoOYRWe/oDeBcJoI3s9MSgKcHVr4Ckz54fh0kDMstrWmwqBsWdcHRDjiZxohXH4DGfnhjBfS3ibhL06B9F7Sch7FOOK56Oc/2Qf0PwRGF/vXgfg9EB6Dqp+AcAJpg4sNS5CXwc4gPSdw38hAsL4MTqglEohqM90BjD/Qr17RzDky2yzVxKI9CwxpofZd0DBpU18oZAGMjTEbBfQB0WzWlJR8TAG7amDopTsRg/zfg0LdkwmqPeepOaXA/7w8gscYKlWjjlrvZdRpIc5n66sU7lg44+dy4byfT9NzpQoUU0ub2Tj8FGTBInNZMFYtN5Y8Fg1Wa0umX4yQixQmwQNzNZU2W4ll3yveMhVQlrf4c/YuzWHmzCGrLW0Tp7q5QOdIOCeslVG7xZC/ag09fA+LLsuiUiKl2fUVAav1fS6/OA9+QZeUtIsTKlkBvN3eFuDMC7QLMAQXQJmjPVI3mdDMMcZGku7cv7SHrrFzTZQBMF4hdjoI7OCQ5kHbWnP6QB9qVO1uBc92y3LH3qalUthzuFxe247iKT9q+V91yC5Qb1+WfZBgJGfT3f11SzkyLt0gMs+N+2HijFPIwr4VhyMD97K9h+CnwvGjls173l+C6E55/VViq3y9irnPnYM9uKT7hUc0toisheo8U99I0AdpAQDWKOA8Vz0LCBQduhymfxLKnpgS8Y1G4+TUom4Ida2CwUmK/5mvRJVh5Do62wrF2OV4iAcThfa+DMwG/2Qhxn7i8q8Nw3Qtye+y4FarnQmIKOp4C3xiMzIXEhyB0EWb9HBxjkGiFyYcESH0qFS/WCRX3g/sZEWkBRNZB/SwYfUr+18ogvFj0AA4ltqpZKq7ks89YrfJczTA1Fxi1WhcCVC+EVZ+GxX+Qqk2IhWDPVyUMMXiYlHvd4RGvTPOHYGKu3EtDl+QcnKcEgB1pqX3ugDDbDGHR25jdFrJ86mgANAHQRDy/O1fTLXdzPJI/DgyyT0+N5SmMKUDLJ+oyraJNwNZlA1mze9Nkb/5YtWkOj4xH5c0C+O4KNVHQgbgVL566JPscP1+QHV9zTZs21Qc9r1osbeEHpPdosRaPwrFHpb+pwyszqrbbYMOXrM8nugWUR7skvjx6xnqfuJBn58j+KjsVSLdbAF3ZIawuX3rFdCwRl/NKF4gNHMq+frqC22TT/hwpQPksHpVUqZ5tcGG71MSdSJuFOjxKBKaAuWlDdpdzIiFgZSqxL3RJgwrnMXnpttm4r87WoOL2/Nd0vFuKhOz7N6uZueESluy/DTbcIwzXq2byhgGHDsGWJyD0pCXocpbDur+FrmY4rlyaCxdKEY/nngPjGPh/CoQh3gxj90NMFdvo65NiGme7YOE+8B+GYDWcfC9cGlLFNBwC8i3HYcEJON8IexdY8eFIBDp6YP0FONYMh+YIOMfj0DgFtx6FkXLYvl72pQFrdkPdEFxYBIPrYXQEVu6BQDdM1sLExyDcAy1PgmNKumMFHwD/s+BQrujwjdDSBgOKzcdrwLkanDutvq7RReJ+digmUzkPahdL6z5zYHN0QrBS2g3awXHhh2HVn0nIw5wURSZEPX3kkczKck4f1K+HmnthsAFOHget1wJee0lLUKpfvbjB/21tRUwk8hXzSK7jtQplFAI7s9OS7gbiQnbypR+Z5q1VTNZnY7IqtlsMGwZJLSprkjixCbAm+4+H5R4K9ktsN1+d6Yz9NqlXo/XyNwrB0t1oSz/6DgRiIyGz4GRVqW1ycZs2ysA+fk7iQXd8fXr7PvWksKbN/11YVjEWC8vMyQRnE6BHu2D0dOEbyVcvHYfSXd6BDsntLVQFqFiLR8S1bAfmgUMwkqPyl69eKbiXTl/BbRhybew5zX17MterX5mW09yeydInJy1QPnEMomdtLuy07ipzf0+psO+W2W82S8Tg9NMCyGefsZbH2iC2DpZ/BDZsltxaEIDbvRte/JnEPk1BV0U7dP457A7DVFBAb+NGYWOXDoPvxwI0hhdG7oNgszDo7m5JWzp7Ala8DJ5BuNgC3ZshHBFWHAqBawreuwviGvxytbBnEEBu7YHrL8DxBtjdasWBV/fC4h44OhuOdcg5NY3Adfsg4oYdt0DMASvOQ91BiHrh0kfEHT3nN6BHIDQP4reB/+eg9UuJy9h7IHAEguqeiSyHwKTkUwPEZwNRC4DLZ8tvmdKkYB5EdfF0mB6Oig5Y/WlY+nErhS84JMU7jv0YxtLA1FUONevAdydc9MPgaVuc96SVh2xargIX7wQrxqXu9JEUJOUz3Wkx4ESssEoZBMh9tUqlrFKmTJVzMeI2zSHjoLfGchGbABsLiegrOAQT5wuwfJs5/ZLjbQKsf5alpNZN3UhcGHdwQDAm2K/a0/anjOnvTEb8o+vFFdp5j+QatmxOLd+4/e/FBTn/ASlF5p9ltRP01RWvwJ1JiwZlgpBk0V3W3yOncncWMa2sKY1Ft1uu74rW0gtjZJxfFgV3/8GsvTcBS8FtZ881i4pXcEcmRMlqAnP3y5kzbf8sqXhlgnPD6tTvmUiICMqMLfceFUB2HssU3Mxaa1X3ql+Z3Q0/2iUhiX1fh4gSEhkeaThRfw9seh8sWiSAFolI2ctXfgDOX1tx7Pr14H0/HFZMvalJGiocPQDex8GleiGP3w5986CqWnKM6+uh7wiseh4cMTi8WApV6Lrlgl67HxqHYUcbHKuU7+ByQfNFuLkHTtTCK0rX4PXCew5DTRB+uwBGqsDtgNv2QUUQDi6GkQUw+xJ07ABDg657IT4Jnc8hNacXgb4EfI9LAZJ4M3gWQkwVK4nXgrse4kfVtaqSCYLpgvY2QFl9ao53bI6Iv8x1AOY9KOy37VZ5hid6Yec/SDGcibQMAlcAAteBdgucDYF2xuZuThMzFhIe/c5ZAfarOeRVaDJi5gCbHoNiREtmGpHmFJCNThYujGHf1nQROzxWDDYeVn2FixRhmVbeosB1lrjAXWUWy8ZQrD4oE4gcwFqU6S45lr8e7aM734FA3LMD9v6z1Ktd9GFY/bnU0nUHvgHPfir39r46awZkAnS2v/0NM6M8Lsaik1K6L5vre+Rk/io0IKwjyaLbU0G7Yvb0Jx/hURGFmeKwK6Xgtns5LmwTt3Z6Wzmw1Nktm0Vta3edT0xYbPn4QTBswGxnR2XNUq2p833STD1d1R6PwKknYPe/QM9L1vJYB+ibYe0fwtoNqlLWlOQg7/wWeJ61BF3Nd0HfWhhWgN/RAefPgf6SpEYBhJbD6VVQ2yglEmtqIHoAlrwqn7++Efq8AvqxGDQNwI2noa8MnpknyzUN5ozCbRfgZCU8P0vVqk7AB49CRIdfrJbBdUEfrOqCsXLYdSMERmCtOtaZzRDXYZ6qWT6+HFxe8CoFdHQxeEYhoUIM8TZJ8QHABfEKcKjB0l0lnXaSaXheiFeLAM9s2OBvhjWfleIbZY0welZKS558PLNvrKsK/KthagOMDNjczWl56HkFSO8QK4b5arqqR50ozjVvApnmEBCLThbv0i9rlHx8ZxqDjYzn7w+cbu4KJZqqE/GXq0yeW81hpVWZseLggALX6QMr/gbxBvrU3/566fzk8ss11lT1sNAQhIbQVn/2dwyIE+pBLaaIxkSPpKcceFjY2erPizvy8fuVy6FR1M9TttdET2GVn908lTK7ygfa5vtMuY+zWXjMAup01/fIicLfKTAnu9o70CFu21KKlkAWBfchycfOqeBenikQK6Tgnrxkxf1NlXa6VS+wdZzaDDULlcssIW7fEyfg+DEY2AUO04Vtm0ToLkmLmqe8K+lVzYZPSJhi/zcgpkQoCZ+kQM39MFx/N7S2SjrSC1vgjYdTBV21D0JXJ+CzVNDhA9IAQo9CrBGObIDqDgHjQEBaEbYdg7AbXlkPk7oUAklE4J594InDzzphRDVYmDMBd16Ek+WwpVFY9PxRuOUSnAnAi63gB+4/Cu44bFsOEz64ZS+4o3BuAUSroVPFvcdXgfsSeC4KwYovsEpHJiqFsRvqfksEbFWtymQSYE4ajTKJu+s212X73bDmMyKIHD4pDU26ns6c2LmqwbkShjrEJe4w3c3vUNdySWaqniMUjA9rDlU9SrmZCwmtTDN7G9vBMBaSWHCx+wABPpMNu/wSPtB0Vac8IkViwmPFNWNIt5zAqho9ODyKoGgWi1fASmgIgoNpf+f2Wr79XdOGAUPHJH/w/POS+7nwIbj934rfRywMx38qLDk4IBf0vidEAJTNokER6JggbQfrlL8vFmaidnOVCaj5czBsO3CbHT9mykIjaQIy29/Dxwu7lyrnZrq8TcAuaywu5alkBbdD3M3pArHy5uyu41gYLu1O7TiVPoC7K2yVwFRjC5df1MfJ2PKrwGHFlrtSt2/cCPMVW65ZbJ1HLAQnfg47/xn6bUVOYvMk33Xjx2HlasknfvZxOPstS9Cl+8B5NwwuhIQmQq3IRSj7iaQFJbxwdCO4F4ni2ueFBVuhth/6AvDSQojGBYzXXoClQ7CnCl6rlQlHyyTc1wenffCrBjnn9/TD/El4cRZ01cOGXlg8ABeqYM9iuOkQVI5D3ywYnwWdSoQ1sRx8x8AREZar6RbLNyqt/O6E3ypFqXuQ4h1md6xy0IIW+/XUwerPwopPSsGVnV+W0FG669JZC8ZCmKgFx0WJ9eoluCTfSVZs6UuHVzHZaPHxcU+VlaZjxFURiyLiwKaZtZ/dFanxViOuSllOWm7hUswOrCaougMSDjPPF2QcMtXbocHs4Dodc3pl/PbWKnd6jSj5vTVoN/6vtyEQj50X4DXBV3OKQnnObdIXdeAA3PXD/PvIZRdfk4d87V/MDNjFI5abY6ovD2j35nbXZjOHW9zJ+Vzj5t/uiumnFoHKXR1KZdF20B46WtilVz3fSslKd337G/Kfn6ngtuc/51Vwl0PDqjSBWBYFt2GIEM6MM/dsy77PWWttlcCuB3+T5P+ePAnH98PQdpsL2xZTLJ8DC+4TJXbLDZZ7feAN2PNv8Ma/Q0JNcBLlEF8vQqPr7xKB1TOPQN/3rLiwowEm3gWxRVJFKz4FtVvArWKsp1ZCcBVc7AV3DNZvA18IjjTCniZxT1eMwwNdwpK/2yoA3RKGD/TDGQ/8ohacOnzqAngM+N4c8GrwoS45xq+WwcqLMHsQxvww2AIdqgLZ1FzwK8FVrAqcavBN+Kw+vobLukbpblD7egAtt8HaL8iAtesr8qyn55A6aiHcDPFyUU47iygveM3ENKeVZ1uMOTxWSUdTkVxM/Nc0s4hGEqRRxTRUhaxSAU53KndzvYC/u0IEVCZT1VDu84jFtpOA2l8aSbKbq0zGLBNMk6Bam7nMWysFRzRVxjM8KucRHlV/j0J4DG3DF99mQPzrj8HhH4gwY+GHpIl8Vac1kB/8Nmz/vyUJ31Npvdy2vz1VmctdZZcHVjNhZr/MnGCdBtxFmyaKwQywbsgE7+lUADMMubHtLNoO2sPH8m+PJi7hXK5vX232c5qugtteqKR2SaqCOzQCF3fYcppfylRRVrSm9ml2z4HTXXD8CJx+DvQjKjXKxgIcPnFhz78POt4rD2d0StS8r/8TDNs6W0UXirhr8x+BwwnPfhMm/kOABoB2mLwNgvUwMgyNR6FcxaIvtUHXddA/DIFxuHG3DEgvzYGTfmHFD5yDhgj8vBrOeKEhDH8wBGdd8GgVzI7B7w9Dnwt+3Ax3D0DHJByqhYQbVlyEiAMuNUKrEpmF6sCrJpJxDzjUAG1oomo234GMrj2GLuIukHjuij+FhhVS9/vC1sywiVYNkRokT7WLZKONa5ZqpTR8SFcjF2uuMstNa4+3mqBTiulOlTpUJYBtB1UDIC6pjbGQsFWTFRcq8JHz3MsLA6o7oOLTatJCwurmZIKpDVDl3f4aLiqU+fZzTffskIpWp56AOe+BFX9iqSVB3H9PPDi9g3uqbK9cIK7+91ZlLjd7T74ZZiTETZIXrM24doEc5XQrbymOaftqi3Q5J+Rccrm+cwGnabpLYrm5XN+eqtTrXrKCuy3TvW0quBMx2TZZCeyVzFreutNyZzduhNhs6OqF41thfIeKK6dtM2szLH5QVNhVnXBpr7itj//QYomJSnDcAKv/VCqLbfs3iP7CcvWGF0Pkdjg/CRUXoOU50GNSAvLAKuiPQnMPrD8taUuPtUGfBktG4NYROOaBX1RAXQQ+OQbdDvh+Jdw0BTeE4LUyOO+D9w9AWIdXG+BdagLYWwONQ6oOtwdcYUg45fggdab8EbngAAAgAElEQVS1dBCwqXJTgBmo2wTtN4gS/uJrmWKeREC8Bvq4vK5ZcWYqnbO1RMy9kbBLXXXoMnNoS4ndmsc2WbCrTDV4cJCMqcaj0qc3OgHB4ey9kosxT6WIsNIB1R1QDSM84o3SzGOb4qzJTOA0AdasolX0NctjrjI5HzuWuAMp2KFt/K9XGRCvXmHs2nug8IqhYTjyIzj4Tblwyz8hbr3d/58wtPn3C7vJuND2/0esZcGB3D0ySzFvtZrR5QDrbMzcvszpm3kwNwz5rsUw7bGzhfdnt2LU44XSvhJxiaePdkmuZ7aCJ/nM6YfqeZnVyJJArRhvioLbfB3Mo+BekFbmc6kouKdMEZgC596dmdvWLRNgrlotTRG6euH8b0FXhUQ0GyMs74QF94sbu3YpHP6RgPKEzZMQXQKtH4TKVXDkW6A9Y7l4J9fC8HUwcA4W7wDPMERdsHMZnHfCqtOwcBCGXfDoLAH6T/cKLn6lArwJ+NwkXNThWxXwiQlojsOPAnD7FDTEYHclrB4VMjtYBrWTEq/W1RiR0EFPCM7mu33tAKz5ZAIT7pffIsVFqkkc2dDBcQ14s1pJLQ5R7NKMt8YK5/tmHE+XQhcuv4TGkp2VTKaqVMeluKvt5qmyANUdsGLEDq8FpLpDlWeNW5XMzPrS9nG+UDpnseatUeN5IMs4HsgyvgfSALc8lazEIzIBSHtprTddZUDcqhm7Dp2WAbQYMwwp7nDgm+Lm03QprL/ik6UfPBHL4l4YyQHi5v+2z4P9xSeD5zNvbX43esrfWdi70zt9MDcMqy5rQabdXdrkZbppX4mYsPqsru8zhduOuQPCOrO6vtvFjZah4N6b20WXnv9c1Snxf7NMZ/fLme4yb63Eib2LYLIGuk/C1F7lwrat66iA9rtg8fvF47Dz69D1U5JMMlED3lvAtxYGngCXSh+Ku2BiMxwpgwX7oUax/z3tcLgM7jgFs0Jwwiss+O5RWBKBX7vhqAP+r6Cw5e944YtBiADP+uD3gjDkADdQHodxF1REhWE7pjk++OdIHHr8fGqM2NCQA4Xzg/k1s5lmdfYpOedZV7m3bsWcNQvgohPTH8tMr6K7QrmtVVUt3XTvquMkYgLasaBVPSs8PH1Xs900XcWO08bLQoBqd0UbCRkbYgowIxNZQZTopLVONG1d+7Z5qoNdfa7pdo+xa/8xGSRLtegknPmNdNi5UrWZC1k8mhmML8TM7etM9c1MLqOvLrcbvRhXe7GpVNHJwurxqT6V9lWCa6uUtC/NIYN6Vtf3mczymOnmrclUfQfa5RqEx8R1XoyCe9YaAebaxTIQhUelGEXPq9nj5A3rwTUfxgwY7JLuUY60c62/ERbcBeEJOPQIhLqsz2IrQFsKsT3gUfsPl0PvGoj0wHzl8j9ZA69XwAPnhf0+54de4PenoFeD7zjhS1EYArY44INxOKpDqwFlBgw6oDYOIV22TyDM2GS/hVgwAE4Z8MIjpMaHkY21N3+suaptWjnNmlIZK/VvIiGu3+mOJ+6AxFFdPotNm0BKwqohHQsJkIZHZqYAitNvc+VmAc4MgHfJd05hnuHcoJl8pQFrZLx093sppjuVR6Es46U98NRVBsQdfmPXf1YxBafXck2YEnOnT5bb/7a/O7ylb/dWVMrKZ/FodgYeLtLVPtXHjBSat88os7nRC4ng0gtdxEKWgjwf2568WFq6Q6G0L2+1VeM26QLvshh1ofxCf4MCaVUu1FUug1B4RDqxDB5Orf6Ucm5KwV3VKfdeZFyU2hd3ZK5b1gZ6G0wEIdoPzrRGIf550HQdjF6AAVu5x1gdhOeIYtij6t+O10J3Dcw/JU0b+rywqwzuUi6773rg/jBUAg9r8CkDRoHTGqw24JgGCw0Y0yBgSKtnVVioJLaarSxkqft4J5vpSr4cgLODVpL5GhYrNUs8zoR5q20CWAWYLr+MBQ6vihM7rfNI3ggJW+5vMJVZ2tlmeKy4xgzTNYdbNYVIB8vyrAAqOJVlmTttfVNtnsM0TbvKgLjda+z6/DRjDJdjDo8Vk8gF6ukAnr4sBfiL2M7hvnLirngkP1gXcrWXUtA8n/kbcrvS8zFzp08G8NBwYfX45aZ9eWtSi8RHxmWf490CmsWUDw3MEVey7rYakE905465e+uEeTt9qipaV2b6huYGRxOEw9L8QLM9F3ol+GdDsAfiw7LMACYbwTMmtaUBLtWAfxIqwhDU4Ygb1oRgCtirwWYDXgU2AaZWpoxUsDQZ8OXYNfC9fHN4be5dwxIdzYS2BVQT+zJLrWyKnHRXGnCax45Z7uV4WFhxTLmYS1Fel2oOTxawzAOUWV9Z1s+mzzESUn8gnuOV67MSt9Huf+IqA+JWzdh1csSqtBILSkA+FrT+j4WKWxYPSY5aPJRnX0q1N1M3c8mmqdmj/woAf559FaN2joWzg3WxrvZSE+5zXR8TzHO50V3llnAlEbN+4/C4EuL129znF0s7dqBNQNOMpYGluAwPS13jQmzC16CKHDjlmoaHZIKRzby1Mps2i8ZkWIV8Rz1toNOqwLB5EcJecEVEQAUw6oZKdY9f1KEpAT1AMxACvEiLRRcQBHz5v9I1uwwzQS0RZ0Y8V7rLqiqVEos1n3Eb+zWBOzp5ZetoO31WWqjJGtNZYgaj9FvCLN10OTuV29nmeo5HSgfGUj+LTk5fdDYNu/pixK26setc/M3P6TVsxbztwJ0VwEuYIOTbl+lueavMPhMsBsDtgF8s8KOpOFLESoGIjOVm5unsvRS2m8s0h1TTcauYk8uWnwjW7N6c1UfHKal1mmneGjKaiYdHChdMcFfIOeYrkOD0y32THu/LliZkX2ZnonHArERqgu0oUCm3f8ojVyyDvcZ0L89MsEkCp5GqCmYG9CK5zFVmFcFITvZ94kY2QT3JiO2AqCYSdteygZxrkilHigc/kwxdbaa7VAEST/aXM8fyQp9nWa61vesqA+LVy41dew8WXvF3ycxOIUUBeDa2n8dLkHU75T56qwrc6y5bGCAHqJtsX/dYTNQe20o+8FH1YCvRSFwpMJMxprHpl6Szm+awWHGyvqwNwCPjlMRuHB7ZRzxcxHZaEesoKwYYs4isjERxTpJrZrcSfpfpmsNrAaPutAG3YoimeCo5izKBPJH2nMSsMpWRSQo2dngrzFVu5f3mA7mZ/izb8lJr51+m5YsRz4iCSdO0O4F/Qubi3zIM48t5Nxg6Bt9os240u1tCc6Qtz7bMvly3cs+yrUuWbfQc22dbN9sxU9Yt4vwKfT9XmdW7s9Tvl75M01Npj1lTtRCzH+iBfbvgxGFoqocbNxXvJUifUETH5X0mwHE6lizWbmMiSSUoagBL2Fx5EUtAUoqALKtppDQZL9pKGOyLYada6rthXAPh6ZmZD20HRbDiqCYgXgboxUOZxU1mwhwe61mYKYBLusYVizbZdNLFbL6rl51l25+7bO8J9Y7t72zrZPs8HpLYdVB9buTZR/rxrsT5ZLznJ0SXDcSapjmAfwXuALqBnZqmPWEYxuGcGyWihfNCr9nMmOawPSzOVNBOAKEwhCMQS4DbAw1OCL0BR07mmTyov826tLkmGpo5WCEDFuplGCQflpSX7aZNxGzvcZVGEVV/R22z/1gmmL6l4QDF5q8ye6sru77trWDVKs0KhegOAaDkBDrbhNr2wj6BNt+1tHd1jOSb8hyZE4K+PpgYB49bWn1qGpT7wVcGXo/1fMVC8mzkBRpVvCMRfYf1an7rbCYY8XrgpGEYpwE0TXsUuBfIDcQNq+FzL6b+8BkzFPuyLLOMXOuSZZtss5Vs2+c7ZrZ9ZruBr/Q5Fzxm2kNkxCEWR9Q6OcytXigVrgfov9bR5ppds+LNUMz2LTwFU3yXLKs+DBPI63JM01NZb1aPXJb3nJ+nrZPhXSxmXznWybcv8/OZPPdS9vFXK3Ne4pkA4hbATm+7gQ0Zv6Wm/SnwpwBtbW2pRfh/1yzprrpC7g7z81LdL4kYPPM07N8L1ZVww/XQ3qbWUcxydAh++QuZaOsJwFB/GyRLNmq2ZRjqf7Us5d2wrW9bTrbPsY5lvif/NtdLW8dclv5/1v1cs3e8GfZ3zfrf/rf5GSBVwLKsb2T5PGWZZi2zb2vY3lOW2bZN/q8+T2hp+9Fsy+z70OG6tdJm0yx+oTthaBRe2QanuqCyGj77edBsn5u1odNdy9nY/LTDdNcewEI2E0Cc7SpnBLwMw/gG8A2AtYtnG7z25eLAI5e/vVQ/f6F9lASMNmBLMs/8MYCrysyJ2bndcC7L5wvezJN5sy1dNnzN3r6mkTrTSh+KzN/XNqFMrmZkWe9tbhNnYdtjmcsrgFXq76dfezPPKItpqXHl3zU9UN7zy20zAcTdQKvt/9lI9mJum7gAr3xpBg59NVmOG6wUl8mVcIdoujB0IDNOa0iLvYs9MNAHkSj4PKBrsGZ1lgmNepl/J+O3ik0bMYir95Q4btSK377l9jsy6L6TLENsZ3qVzPv5TTZXuVL9K7W/qfpPpgIpMZNd1JRkm4qNOlS6kGYyU3PQzsFEMXKHsYwEHNgHZ07LevEozKqHlmZoqLNds2mGzkpaN0u4L5n5oEJl8chbWNPh6rSZAOKdwHxN0zqAC8BDwEfyblHeDDd+oUgguQJxhxkBPlNUYTPDsFJtZirpPNdnsckCyeolFjCpSfv/xOnity3FdFsxAvvgCmBW87E/wFeh8OmaXWEzJ7IY1j1wuR4nM43OXrvY7PaTdJ+aAiibYNCeL2uvVfxW5MQ6/SrnNUuuf6UBjW5oaJaX05+/NHCx5YJ1V+Y4N1OWnoJVip5n2tqaaRwrn06olGPx77l/2su/lkZM07TPAc8g6UvfNgwjR1FeZWVNsP6Ll3tokrm5+QDJLKBwJYHx7ZKsnsxTNFMLHHkA0Ui9Ie15ivEIyQIesRKr9yTUtkWbSgcCGwu6ZtMxe0EPIwKaG5KlLc33mTRTEVwotcehBnwMeZYSUaQEWBGWbFrvU8Bq3itKtBgPSeEWs8Le5Zi3WuqRuwLgqVAlFMtVnWUTwDwWGzbZruawzik9bTBbrYCMlMCgKimpykvmMg3oPwQzUewuZb8Oq33rdEsDl9wnwGP9lr8Ldv4lrigQAxiG8TTwdNEbTFyAF/8qN8AVAsDIODPSinCm7bKT1d1gT1cw3cfJlB6bqMp0+aawZPtDbit4ERouMae1RNNdVoJ8EtRt1YMSUUrui5q0qzMd6G1j9uIf40AAjBBoXqQNolstr8AqfwkiCLKL6wwnaGnPnOEi2S/Zbq4yuQ8i45CtapTTJ88Kmso5D+bPo/VUi7jT4RVQMFR1vNBQaalq7oDqWFYthVvcqlFCspk9lus0OpFaCS44IM9RrrKlxVpK+1NbXfayxtz12c11XAE5z3i4uMI+xVYMzLevyISMJW9VTYD0qmDTqfdf6nZXokHQrq/k/fitaUk02Qu7/9/L28eVSFYv5jPdlcYQzX6bNuAr1IorOJi5zky1F8tlZr1XM5ZlZ8RAEvAT5neL2B7MAp1Qis03NN1cZqnRa+w2v81EaUkNSV8pB20UCIB2ClgKHAVWICB81glzFNAO+aFG/eZRFyTc4LGBnaMOEhOkpMQlPKD5QQ9lAqPDI+EozSm1u4MD2dmpr17KlDr9ci9GJ6QpR3hYXrnMbPDhVe3nHC6ShWwiY6obWK+AaJ5+sSlm7/ZVu0R1+apTzUqU29dkvfFw7sYr9mXBfmkucrkN7e3tTws1WalonX77U7sl4pkgP93JQFHbqeI6kfGZ6V1cqpXUIKiIcsEF6ma8NSUul7QZux79u9LKkdlZY6HSZIl4/h6VuRo85/rcziyvJDtzB6w+nMkOKQo4zQo19lJJyX6h0bTqWUH5TuFRKQd5uaY5VOGOtK4wcdV2cNqAavpEr1nSMsB3GtfIdDPHkWCRAmIOAsuBp4C7ESa8ywG3xGWdI+WwToVYuqtkmypVaSxUBbEAlJ2zzs9RB4G5MHURwraBxtAg3qjct2EInc08x+qFUN4i93ZkDIaO5mZdlfOszldOrzyDoREYPytV+gpNAqs6rfaWvnpbY3iHPDPpbTsne0trZpKt21euvx1eq855sV3S7MtmrJf5DLc/vVJmTqhKaQyUreRvKc2DIuNXxIN49TV9WLvW2PX6jiKaOudglPlelzvbLGQpPThz9a40Gw4oxpkslh5PY9E2xhmZyJw9z8QDZwd0e9NvIyEuPhPAw2NMG1B1t/qeiRLjv9csK+vVPcpjUMKkz9xPVAOXAcM6VCfguA4LEjAInNBgowE/dcCmBMw24BE3rE/A/Bic98CharjjEjgNGArAQAe0nQSvYrlTHaC1gPsoOGzNOhpuhfr50LMXhl9PPbd4C9AIVbXgGoWRPZngWT4bZq2FitkCkqFh6QHdvy93bLd+BdQshaq50ozD4VHtJs/C2BnpST10lIL3dfVCaVcZaFc9qduFSXoCMtE1gTpXq86Sun0BFW2FAdtk+NmEUvGIPK+5wLpQJ7WZ6mWe0v60Kg+I5+ioZtaXv1rNbBA0rSZAadudeAzt8yNXGRC3asau/3QFD+CtLr7Jc7bmzuhZpPdKNZm82cey3PRj8j5TkwGzXV4S2F02VmykClJMFnw5x3b6xa1nqkcT0cJu6WymOa7FdXOZAVLdJ22S5Q6A5oFwCUzMBN+EJsVVgg7wxWHQAbXq+m91wY1R2KFDXIPNcfilExwavC8KR5zw63L4xBhUJmBfNZyph9vOQSAEETccWAlzXFDzOjiU+zq8HnwrIfo6OPZb5+TrgBV/BBVNcPwp6H4GEnYXdhXEFkBgAdRXg3YOhvfCeFpCu+6Elhuh+XqoXiDP5VgXDBySV9+e7NdEd0rlvtplULcMapdK/DUWlO1Hu9T7GXkfPp7/GmsOOb4J0JUdqaDtrZEfIjiUH6zNvye6i/hhbVbeUhzT9tWWJm6y9zLP5kYv5GqfkV7mWmr704LMPIsL3uEqfJjLtXgEXvwLua8WfkjG5FLtO4vR/vjoVQjEf11TZKPnEppBmzNiExBTbqg8wGkuDw3PjPpZd1quH3fAyjtMpu7Y8iHjJjs2ayRPsz2f3TyVpDQYNxKWsCsyWvr+zC5CZq7wNSvNEl4gBnratfPVg78FRk5DXMUuszFkW0nhjM/iGjgMGPNAIAwhHfqd0BqB7V5oikJHHH7ogTlxuDEGT7vhgAu+OCn7+2otVGnw0QH5/8U5MFQHG09Ds4rNnloD4YXQdhzKd6vzcoHxbmj+PRjaAqEXQTfdyzp0fAA2fEHu76OPwcknIGh3YTshtgj0ZdC2EepiYHRB32vQuzPzOtYuFWBu2QyNG+TeHnxDgNn+ns3cFVC/SsC5zgbS3mpxRY92WSzaDtQjp7LvzzSHB6rni+u7st0C7CRQV6X9loaAWhKg87DtsbOUxFzLGguz7LJZEmOeCUFSRi/zEl3tM9HLXNMFzIuJl2dj5Z7KwtdivBu+twxm3wzdL8OCD8DyT0LjuuJTu578INo9P73KgHjtWmPXrl2pC2Oh0oHTviw4MDNiJ1eZzHLtP6Q7IG4qpy81x9HMNTRZqelGDw1LvCs0eHkzR1+91UjbbMuHis2ax5sOA3aVWSkViVhprNf+3a9ZdkuUC8g4JoA08C1vhYY1MDEIfa9Yy/MBcMq+HaDHVdhYMeGBcqhTE8jttXD9IAR1+HYVfHZI9vMPAdgUgpsjsMULO7zwwBQsicALFXCgCpYG4fYBAfdnl0OkEhaeg4UqxjuyBE4vg44a8DwPfsUmE5XgeQCWfxR6XobzPwWXrdR8xSJY93lY8lHJmDj5BBz5GQymjwHtwpbrb4b5a6FmEkJHoOdVGQDThVbeGmHNLZsFoGddJwPz8HGLOQ8cgsFDuQHV3wB1K9IAeokAN4hreqInFZzTQTufucqgal4qow60W6BtHiebGYaMJ/kYtvn3eHdpcU1fXSZw+xos0E6Cd8OVdSGnj/vpbvRCzHwmepnbiVM2Vh6PwLkt8PE35F5443tw8FvCjJd9Ehb/PvjSCzFkWr42iG8NEHcGjF1/P39mLyYoAK2ygWdldkDV3SQ7A8VN13PIUi8HBxWQqldw8DJmb5rkTXsCNhdzOlMNWUx+OkzYXWmJ2AxVWccs+FGsOZT4ouhtTIp2zTBcEG8GbQoco0hekM0q50LH70mu68HvQkRNzgzNSg9K2R8WANvThgwHaHGI+ME1Jev01EHjoADytiZYMgjVEdhSLQKs+4bhjAt+XAkbp+BdU/CSD7b7YW4cPjQCA054tAVcbrh5EBYNwZgXXrlOwjh1l2DVQdATEG6CrpvANwtqJ8D7LDgUy423QOCjcNPH4OJx2PcNSGwHXXlhNBcs/Cis+wI0rIKpATjzNBz7OXT9KtXbEq8TUHauhPm3wfwFUBOHwd3Qsx0ubIPhY5nXrmmTxZqbrxdAAelfPXQkFaAHDsrEIJsF5kDdcos51y2DmkWZiuNETEDQBGo7ox49U9gV7amEys4cru92AfJiLTpV2DU+dUnApBTPn6dSxrB8bNt8n44i+3LMMGT8LIaZZ11npLjUrFWfg9u+ajtuAs6/KIB86kmYdy/c+d287PrqA+L0GLGmp6r4UoAzPVYQkHd3Bckel4mIpWpOAqgNTIO2ZdMFfd0pN6PJlu1x2yRTtQG62ax+ooeSActbYwmsNA0S5necyp/GkW4Or0rlwKoOVIxpzmsu6EIWmwOJADiHQL9EKvPVRAC0+CMymO/9Jpy3pdkbbtAi1rrm/ZELgGNl4FRiqWAj+Hrl77Ot0HAJfBE4OgtGnbDhAgy44SfNcOMALJ8QxrunHNZMwC3j8GoZbA9InPgTl6AiDo/NhpEKcGnw3i6onxKQP7pOns/yKVi5B9yjEPfB4L0QaoCqSnAehbIXwFDPVnQxNH4C3v1hGB2GV74Ng78Clw04q1cKIC96SLw+sTB0vyhs+fgvIGgTQBleiC0UYG66GRasgPnzIeCAi69BzzYB5+6XM3+nyrkKlBUw1y5JzboIjWS6t/v35x6cqxemsedlUD0v9wAcj0jqymiXxajtQF1I6OWtFTFaNtd3YI7kxU7HYlnU4il/m5/1lpZDbE/7KgTcpUwyrqQZqpBMBmArsO55VdLfHlDP8OQlOPc8nH8ezj0n43LbrXDXI3ld1VcfEK9cYux66UkFqOXyRewM1M5EM5YPWsunYw6PUiTWiDvBU6OKBXgs928KU50QN3l4SG7O8W5KBlZ/gyit7SXjTOV0ZEK+S9GNwXXF6tWDb+ZKFrWpyh2+VjqydIvXQrxTANJ3CYyzaZMVHeqWwtKPw/wH4ciPYM+/QFCVXTc0MDySZwtyv5kTIwNAsV2QmLK5XqxGwB5gciGUKTA7vQCqL0H1KFyqhtfmwp37wB2HX82Gc2746DmoiMH3G2HICSsn4JYR2FUO22vkPtw4CutG4HAV7GgGtxsCBtz5BrhjcGQejKyUwcqTgIV7oFwJq6buhsmlsh+PEyoOgvaMVAwBiGyAzj+D2++RyeT2X8Ph74BjJ+iKkeleWPbHsOazApIgx+o/AKeegBO/hP40YVasU0DZsxoWbIB582DuXHDp0LdPQLlnG3RvzfQwOX0w+yYB5ebN0LQ+u3t4qi+NPR+C/r25C9PUr7AEYuYrMKewgCoWgrFz2V3fI6cLe+L8sxSLzuL6rmibmTSjeFTOoxDTvhJpX37lLncHpl9q89cfk99h9eclfFGqHf4h7PknmdCde04wYPbNAr5tt8l9W8S5XX1APLfM2PVfmxVrLYHh2c3ptQDVWyMzR1+NVM1xlYMjC6hGJoRRTvXJDTPVrxKtS7wGZU3iAneVq5J2TsU6TfAel+9Vyk3pDggz0G0M1ow5F3U9/HKzJWLFgbrmVGB8zb2c1QwPxOZDrEMAyX8CImdSJzCaQwRAK/5EwOTCVtjzr3Dq59Y6iXKpPqUp0PVUp3o1Ej7QVXpOohp09Vm8AbRJ0Cch5ofgAqjYJ5+dWgn+QWjqhkk/vLgS5p2Bhb1wPgDPz4GySXj/aRh3wg9a5WdePA63DsCBCnilXvZVnYAPd0FUh8eWAy5wOqF5Eq4/KOvsXAuuRRAOQ5kfZh2A+r3yWWQtTN4OZQH5nCA0H4bxp9R1dEH4XbDiM/Cu2wTo9++BHd+F4PPgPGldi4aNsPbzMpGxA8hED5z+FZx8HM78KvV3is+y2HLrJliwUIC5oUE+HztrubJ7tks6VLrVr7Jc2S2bBcCyDayGIeOFyZwLKrhdorS1s+e6pTJ+FAsq0SmVjtWVxfV9ujAhKW9WbLoje4rWTKuOE3HxOhbjIn+z0r6+GoDr/gIOfUfS41Z/AeY/UPx379sPr/yN6BHaboVZa6Yldrv6gNjumnb6Zdbjq7WBqnr5ahWw+kkF1aAAXRJQLxNYy5tFqOAJSEzMrHOaTCafkiTv8BCMdRefK6u7VRECv/XDmQAbHCyOlTrcqSBbDPs1a9zGIxS+FteKaiQt1gHxuSIaqp0EbScEz5ByfXSX5Luu+gws+ogMhIe/JwA8fkbWMYBEPTgGrW3LZ6t4pPo9ElWgq2IZWp0UXtGV+zm6GFxH5O9wG0RqoUIB38n14ArBnAMQc8BW9Vzf8pq8/2oZDGiwqA82XIIjlfByA+g6dIzA7ZfgSAC2NQtL1XW4+zw0TsLWNuiuFyB2OGBxLyw+DVE3vL4ZqjsgFILKSnAdh9YXhcXHWiH4AajrgOFhiMfBOwVNe2Fgi/q+lRC5AzZ8Cm64ATweOHsWtj8FXT8G927Q1ITEWQEr/wRW/pkoku0WnYKzW+D0k8KWQ7ZQU6LMAmX/CliwTFzYHR1yPBDvVu/rFjhfeDmT5ZY1QcsNFjDXr8o/aCfiAorpArHBw9nXdwegfmWmgttXm/sYuSwyLkCdzfU9crJwVaqK1lRGbY9Tl7dcmS+404MAACAASURBVHKPphmJNyft6/wL8IUpGW9PPQF7vyqCvpWfhhV/KvjzJtjVB8Qrlxi7nvm+AEVoyAJRE1BNcJ3qlx+gVIWuCaz+esVcy6xYrpGwcoIjoyIYmeotTSTlM/fry2SwxQb/wUoz0nSZYEQmimOzTr/M+GLBwtdGd13Z0plvG8sy4Yg3KODtBHcH1J+FyDaYPEPKBMbhgaaNsObPofNeufYXXoF9X4Nj/2HbXzXgBYdtpl+zCIZPWJOueAM4lFhL80G0HpzK1euYByGHFUsN3QDRUXH5Apy8STw9Hc/L/wc3wWAtLHoNGvvhRCPsbZMJ5E1HoWkctrTChSoBx9YRuKMHTgRg62xwuSAWg3mjcGM3XKqEV5cLEDud4HTAsj2y76l62LsJZjXD1BTU1UG4G9q2gGNIQDD4kMR+y8rgnPpObYD+K0shHW+B+F1w0x/C+vVyDmNjsHMH7P4+GNvBeca6fi3vErd1572ZYGgkoHeXgPLJx0V8lfwMiC+wgLl9uYDy/Ply7iZjSsSF4fZst8B5NL3zmAazb7TizM2bigPNeKREBfcs5eJeml3BPR0Lj2amZJmu7+ETuYulmJbN5W3Gq8ubS8tdvhy7nLSvznvhvl+m7q//AOz9Fzj+E+i8B279FyFiV9CuPiAutaBHebPKuWyQ9xSWqaki8CGIqHSeqUsCrmPnigchp89yOZtpSmATgo2IK6UYNuzwCJN3egAFstEJuZGKOQ+HR6UuTBYWTTk8lqcgr73TVM4OMipTJfwQnwexuQLAjW1QsQfGt8LEmdR1nX5hRdf9BXS8R5aFhuHwD2Dv12DkqLVurB2cMaQ1N4AmrLl/v3W/xGarWK+ZKrYcEmdUrNQBjjsgshsc/SLmCj4Axj4oOypq6dO3gbMaWn8m6UsX1sHJRvB0w8a9wo6f2whBTQpo3L9LfvKfrIS4E4JBmD0O7z4PXZXwwmzweoURazF4YJ9U03p6NYT9ApA+H1S4YPnz4JuQ9KXjy6C+XvbX0ABTQ9D0ArhOyNcK3gPaeli5Eo4ehYkJpL+1Gy48LM3rQVi/831w64dg1So5j3gcDh+GV59Q4q7dlqjNXQOrPiUMprI9+08+dhZOPSWs5+xvUz+LtwggxxZC+XxYsMBiy+609JzJXgXKKtZ8cUfmsWoW2YD5eqhZWIK7eRIGj6S5uItUcJsu7pqFl69QNgy5p1MEZLa/h48Vbq5TNS97oZNAu6RHXW4LxVio9O9pT/s6t0XSjT7yqoyTQ8esMEXPdhnTmzbA+34qxOgK2tUHxHPcxq7/scQCVn+9qgFbYctvjUrtz/AIBC/BxEUB14mLpcVeTReFmT6UFDlFrUpZwb7i4xW+OnEtJYtcKJCdulQEO3XKtrpTZuKR8cLAblb6KlTT+Z2e36s5lXg9beCIdSrg7QRXK8xtAufLMPiC1Cq2m6scWt8F6/6zCHpAHure12H/1+WBTrqWqyHWDL4RiKsB1FMlYpAL260a37EOcAYBpXT2rYCxqOV6rrgOBhrB/Rtx8yZaYOo+cD0DnpPScOHce8HdCLWPgGcChhfC3rkCpCueh/JROLwATjUJw20YhM1HoS8AW5fKsnAYWqbgtpPCkJ+fI+Dn8YgbevUpaO+F4x3QNV+AWNchEoH6BKx8TqqBXboVBuZARYXss74eQkGo3gkepVqOrIXwnbByjex7j4qhNjXAwkHY/78hprQPkQ1Qdp8IuhYvtgbu3l7Y8Qq88R/g3GV5DQDmvEdCA3Pvyu06DY8JGJ96Ek7+MjWkkwgoprwQ4nNg7gKLLdfWZoJHLASXdlsD+IWXM7UtnkpVCWwztFwPs9aVrmi2K7hN9tx/YOYU3KWaYUi812TR6a7voaP5tzfPMVuhk8p2GfPzAXVwEL7ZLt6oDV+C1ltKB/bjj8FLfyWx+Z5X5XcyhXrN18t1K9S7YIbs6gPixS3Grq/eZwHrlKpsUyxjc5VL0L2sUTFYv9XPNBG1GOxUH0ycL65NmqmmTtZA1RRYT0gcKlxERSpvjQJOBdDh0cKuZleZAuZY4fN0eKxWiLnsnVJeUneqAvppYrZ4owW88TZoboM51RB+Gi4+m8k6PFUw53ZY90VotD0j4TE48gjs+zoMHrCWRxeBVg7e0xBTA2RVp8T8urZAVA340U4BIV0VvfC3w3gnaDskFqy5oebjcHE/uFV8N7YegjeB7zFxzyb8cOEe8M4G7w+hohcmGuDQZqioAvc+mL8Xpsrg9ZsgmhBWuegItF+ANzrgWBNEo7K8KQS3HBYX9NbFAtCaJoywbhJu3AdTXnhxE1J+0A/lqpyf/yQs2SXq7/MPQqxBtkskoKpKBm3XMTl3LS7XPvgBaOiETZvglVdgQMVzN64E91bY+4/yvynoqrsX7nivKKBNCwZh3z547XEIvgCuPVZal28WrPq0VDmqaMl9ryTiMgifekJe9vxjw2G5r+PzobJZ2PK8ecKWXVliw4Yh8Vc7s8pW0atxfWpOc3lz7nPMZyUruFemisOKVXCXaoYh55Z0eWdxfeczzSHMPluhk0C7bL/lU7DmP8Hr/yBj8/q/lpzdYr/LZC/s+WeZIDdfD+VNl/GFL8+uPiDO5ZquaBX3cFmjME+nTwRP2ERToREF4BcKtpZKmr9R3NnuChvIqp6jwUGY7Cm8D1eFlEfTlRsrHpKZaqEYi6tcAIOExIDzMWDNocC2QFvBgnHf30EBlulNSGcHRoWN9c4FV7UMpC1+GP4pnP2N3C9289ZCx12w/osyUNnt0h5hv4e+Y014ElUQXQp+HYzXIaEU0E2boHaxiIbC6rxi88CoErcqhhTx8N0Nw0fAdUjWabgZhtdB8MfgPA/o4tKNLYDy/wDtPMQD0P8geFsg8RjUHBGXcff7JY48cgnWPyfdjQ6ug+6AJb66aRuUheD5NTDskeUOB9ROwc37YKAStq9U1089/xpw627JF967AYItEieenBTAnTULyp6HpuMQrYCu+6GsTv02usSFvV7ptFT2E1XqMgCTHwStDe66C8bH4cUXZZvqarhtNXR9DY49qq5zJYRvh9b3wR13QLMNuAwDTp6E17ZC1+Mi7nLYJlWd94q4q/3dhQfp4RPClE89Ad0vpX4Wa1OgvBAStTBPMeV584Qt57LQsLiwTXDufjlzQhyYoxizycaWT5+NmQruJHt+YxoK7mUz4z7OeY4JIVq5XN8ZsfgstvSP4M5vy2Tq1OPw2v8jhGX9F0Us+WbUmp4hu/qAeFGzseu7n5F/TICdUoA4cUEKwBfTg1J3yQzKawNZUzgVUSA7fq4wK9V0KGu29TJNiDozOCipSPnMTDtCExFYIaGW6R43ux7lMvt3yXne+djv2ygmnO17aE6ZPIWG0iYdeqq7OVEHTc0yWDYA574NZ36TWfrTPws63wfr/waqOlI/i07C0UcFgC/Zyi5GF8lxasdhaqu1vPNecQEe/qEl8ovNlUG8/CDE1LEb74ezBrifEUWwwwfz/gvsPQ2+n8kyVxOM3AuGHyr+A4yLEKuDsYfAWQOhF6BhKyR0GPoYnAkK4DXvh9p9MFwPJ2+BWFxcxa4R2PwKhNzw2w2poFQ5BTfthJEAbF8rA7CmCZDqOrR3wbyj0DcbDq+y2K7PJ2ro2mpo+zX4eiA8F7rfDZVKCOZ0qhzkAEwO/v/snXd4XOW19X/TR71LVrPcu9wt925MtekQwDSblpBygYSE1JvcJDc3DRJCAqGZ3kyxwTZgwDZg4yL3blzkKstFvYymfn+sc3xG0sjGQBLnC+/z6JE0c+aUmTPvetfaa+8N7lfAGRU3Dg5SLHjYMHj7bThgLKIHDYIBqfDJDwVgoHhu81TodT5MnChzVfSorITSUlgzD1gBrnWcbKKR1FGA3G+mVVXrVKOpEsoWWsAcvbAOp1tx5VBHSM+0JOyioths2RyhABzfaMWZD33cVo1xuCF/nMWac4d/8Tjl53FwZw9sZRDr95lKNn7hEQ7pPWlP+q7dB+c+Cf1usl4TiSiXd9X/akE18mdQPOsff65fwjj7gPizmLXis5XyEZcZBbIRA2TrBJL1hz6b29nMN45OAwrUyZV9uiYIZttDu9NwNteefpHgSdVxgr5T13F2eARCp9rG7tR1twe4Zz0Yx2DnDreRWhU1bA5Jd4GGGKy3APydDLm5QLE3Uz5MqYctD8K+RW3NcIn5yhcs+UFsWfDYJtj4CGx63FoUhZMgMBiceZC2C2qjmg/0v1UT/YaHrUk12AkCxZD2KfiMmFnOaKgbCTULrJrLHc+HwDQoexU87+sx7zA4NhlsjZD8PISPK+7smwGROPBthqxXtW31pbA3Hjp0gKM7oP98sEVgwzlwwqVYr90O2Tuh6yY4VABb+wpMQfdQQiOMXQ61ibBiVFsgdvtg1Hvq5rT6IqthQV2djFmRCPhPQN93JK83jYPjgxQvDoctYMrMhGYfNL9pxY2Dw6HpHMjMgSuuEBC/847k8bg4MWbPTlh6L9QaTCnQG5onw+CpMH68QD56BAKwaROsXAqV74OrFBxR80GPq2DA7Z89thjyqwiI6cJuUUfaA4EeBjB3A7wWKHfvLoZ/ulF7wCo2cni54s6tR1Z/ywCWN1oy7ZfBWD+vgzuaPWf0+eydh2r2ap7M6v/5z/mdWVqc9Jspk9XRdfo5tl6FWxxu6HUNTPjj5z/GP3GcfUDcyRsp/b8R+rDdCeq/SsSoNFUng0D9IcVhTjfcyWKznmTDXWczHNS1ig+criSkJ0UOZ9N9HGjQ604l7ZptFG2IOZ+q6IbDawHPKRmw16i01M7ncUo5+lSA+88G4xjHc8a3XWzY7IoDhQNtQwy2dGguEvAGOwMGAHXrpkmPMlj7R+UHtlYskovUqmzo9yC+FZMCGQB3viIANhkYqHiHfzBkJIJzGdQZoOpJUQGAuCxY80drcg4Wgn8EZB6FRkPeTCqCjJtg2ybwzlcRD2cSDPsNrKiCwNPgNGLG7ivgRB+IqwP3ExCuEajbZkJjCAJHIHU22JuhZjQc6SPAKy+H3mshfgcc6QSVk8SEq6vFTAevg/QK2DoUjuUKIM3vuLsRxiyBhgRYMa7lBB8KabshGyCjAg6OgEOFArsOHWTaamqCjh2hdiN0XajXNV4D9YWWA9vt1vlkZ4slH30fvEbc2NEdaqZDJBGmTdPnuXCh3NWgxdV550DZC/Dxj63P1l8C/vEw6hzlIMe1MkFFInDwIKxcCVvflmztXM/JcqGp3cWS+9742XN1IxGxyN3zxJbLP2n5fLCzxZYjaZKto9my8zMYpgINUL4qqhLYh219IvHZVk5z3mjJy19GtazoczixrZXEfSoHd6e2BrH0Xm3P6eWJurZuF8OoX0hBOtMxZ6oWD43H5AHIGqjrzx4kFp/Q4cz3+S8cZx8Qd46PlN7t+mzFKVK6GHm7SYrPRsJWQY+Gw6evHe1JtdKdwIjtVp3+dd5MA9gNK/ypzFoOr+LZkfCpGfZnYcDRpQ/bDIPBxHRGf1mA295+YjzeXk1qd1Js1SCthwC4Zk8rRuyESA+Bb7ArRNKVL2ummHTrBic+ERAe+rjt+5faXXWdB98N3nZyAU9sN9jvY9bCKRwPgSEQLIYiHzQstGocp3RR6pIrAVb+GqoNmTWUD83jIMMvxhf2S7XofRfsiIemF6084G6XQ9pMWDIX4l5S8wN3OjRfLdNVZhP4/wKRRgj0BO8tUF2vEpHxj4HzBDT0gsbpUF2jyd1bAblz1IVp6yVQExZTjESgqQ6GvaEGEJ9cAGEjDc5kxU4fjHoXfHGwYrJRYzdolK/06CerArp+BLVpsHmiANXn009hIRw9Kqe0YyVkfQRhFzTcARhSptutn/p6bZeZCTs+hLgXVDXMmQ41l8kd3q8fXHQR7NkD8+crHu1wwNSpUNwdVv8GSn+n/UacMnQxGsZPgeHDY0vD9fVyaa9eCr7litU7orIses+A/rdLCj4Tptl4VNW9TAm7hQrVAZq7CZjD+fqOR7Pl1NR2d9tiRMICRdMAdnhZbMNTdJw5b5SyTr7sEdPBvaH9SojpvVo2yFh0G1y7SvH/NQ9AjytgxE9ObaprPap2iRRlD/hiudRnyTj7gNiUphM6qC1cXIbirDaH4gamiar+4OmlZ0+a0Y8y0Xh9QI7XhvLTAJ5XsrfDrS+Vv+7U8V2H17oZAvWnNmm5kw12fQqm7IwzXI/tMWB3+/Fh02X9jxrtyd0ObwxWb9NiJ5bykNFXr4n1OTq7QkO+ITfnAw5N+ubklZ8PZW/J8Vi+otVxbTJJ9blRXVHc8bGvI9gMu16XlBxtygl2FQAn9IIOe+Doq9bnmTsCht4j8Frxcyu2FuogIEhNBucCaDRyhntdD82TYOtcgwUHwJ0GEx+CTcCeF8D7prZNHwYHx0MoAToGoOp3QACC/SH1DiivkNzseUF5uYFcaLoZjldL+iw/LCbqOQIHB0BonJhwXZ3czSlHoPN7UJ0Oa4ZbcrXNJrB1BGD4m+D3wPJzxHbtdjFMt1sgGAlB8avgCsD+q6HGa4HwsWM6jtsN/mbIXQreLRDIhsaZEGeUuUxKEkhWVoop9uwJyz+AuNesuHHwCmjqq+u68kpIT4dFi2CNIdcWFIg1exvhox9GGbqSofkc8JTAxEmKMTtiGJ7CYTHtVavgwFIBsiuq4EdGX7Hk3jPa9gw+3Qj6pMbsnicJOzr10ZYA/u6GE7sL4NaCxFxQFhXFPt/2RuOxKGBeroVo65HarVVji97/mEIbpku6dYnPWA7u3JFwraE4NZ2Q63nz49BvloxWn6eK2L/5OPuAuFtqpPQXvRWMP13+ridN8T13sgGahnzcdOz0rmmzo5Mp656uGbVZiMPu0I11ql6/rkRDcm5uP+3I5jAAt6n9OG5McDNf7wTCsRnwqTokmS0WY51PrPOIBew2h9631ufm8OizaDpOm0VElrFybTwOVa1yDF0dINAZmgoNudmQMqNZb1ISbH8e1v9VpqloKd5ml8u03ywxGmerIgzRo3o3bPy7fsy4ccQL/iGK/xblQ/xqOPCq9Zqu02HId+V+Xv4zrf5BlbD8EyC+I6R9BJVGqlHuSOj0Hfh4A0TmWADT61rocS/MWwj+l5RiBJB3HezoAtihN3Dw58b+h0PuN2D3Hk3QnvfA8aFqVDfcCjUROZKPH4fcI5A4F4LJ8Okl0ODXJF9TIzDuvhWyd8DhgbCnk9iu223JpLYQDHsVgi5YOkUAnZCgbex2bd/YCD22Q84OONYXyvppUVRdrYk4J0fGrZwcqD0Oua8qLuvvD43TZN6qrxcTdjqVD5yaqhSmdxaC8wPwGMY3z2Q4PhJwwHnnieXu3w/z5sEJ47s3bpx+jq1RPqgJRKF8AXLKIJg0Cfr2bZ/hHj0Kq1fD2o/AvlbStb3Suq/63iRQzhl65vHYSERxS5Mpt3Et9wKf0aQikqzP2FxsduumcqFnMoLNOt7JjlMftZ3TXIktK4HllvxjOx21dnCXva3F+cWvtdyu7hCs+B+Fhgb/Fwz/4T8th/dsGGcfEEebtTwpMsCczMHFkJ6rxaROBYY2u1Ke3EkCplCzmFnDkfZfY3dbTDgc0GqtXSC0qzuTzSbG3N52Dq8hKTe1NSGZwxkvEGxPdj4VIJ9Krm6PHccyRJ3qOK4EOT1bs3B3itSKWAVLsgfrvfTXqNRgNMjbveDsC7VGXm/EkC6j2UHHjvJybX4CNvxdJowWTRWcigcNuF3xvVMVKggFNBFueFjVdMwR7CT2ay+GXvEQWAQHF1nPF98qCbp2Lyz7qeWaDmUIgN29oWA7lM/R4wkdoOSXsD0O9r4InoXKa/VmwbmPQnk6fPAKxL0sgHLEQfZdsNOQUYfYYefP9Hd4EnT5hgxHNhuk7ILQs8rVrb8ZGjM0ydlsqhqX+5TaIe6fAHHD4fBhgWdWloCy+2uqgLXnYqhLVunIUEhg63QCERj0vBzYH18kAI6LEzgEAgJhrxeyw1D4EgQ8cORW8AXEivPzxYqzsgT8KSkQOgrpT0oJ8F0IjFT+cU2N0o8cDhmzEhMFtm+/Db7VyjcmBIn94chUiCSIOV9yidj0hx/qB8SWp08Xm9z1Bnz4PctkFOillKcO/WDyZOjatX0wbW6GDRtg5QqoLjVYcpSbOHuQALnXNZ9fCq07CHveEjDvXdDyOUcRNHYSWw53AGwtVaDCwjNjy6D7o2ZvSxPYsY1ttzPzaE1wTi6Mvb/NT4ogDbvXyAb5HGPlb/R96n+7pPXqT/Xb/Dvok3x9zfJ/XOrUWTjOPiDulhop/dVAlSCr3nnqalDeDKONYKI+tKBPrKXuFEXAzd7BZv5uc+2pmbBZFCQSEvC3J/u6DPd2sKl92duZIABvL+3JYZRriwm6NgN0YzxnsxsMNQYgtweudqexQInxnCfViHu3+vzjc3SN9eVtGXfOUDnZg40ydLRWM+L6gK8Q6gsgnAcYsqjpcDbjZUE/bPirAPjElpafv92tFfzAb0KPK8XUTjVq98HGRxX/NeP+EbeYr38IZPeGTnVwfA4cNWRPVyIM+S8YcKeOv+wnlhknnGbEIouhZxUcftz6rEf8BBxT4P254HwDnIa7t+9NMOx/YMFi2DffMCcFIaMYwtfD/gaByxA/bPmFceIXQt9vwgqjfGJ+CGp/qb+bLlfespkXXFcHGevAuwT8BbD/QvA1i5UeOKB9Z9ggb7Zk50+vAadLwNrYqMk9wWBEfZ8Bexg+mg7JKXptJCLgdDrFZP1+KHwNEirh2EVwJEOGrcpKAbfLpXPzGDFoz25INhYqDbMgpVjP19SoOIfdrhzguDi4/HJ4/32o2ADxL4GtErzZ0HA1NKYr3n3llVY8et48GbEAhgxRfrHLrgXXsh9bXgTT0FXUB6ZMkbTd3ohEYO9eydY7SpX+5CoFu+FZcbjl1O1/h+KTn3cEGqBskeHCfqNl6MuRJkBu6gKhzoBR3zuaLbd2iX/W0VyjPs3RlcBaL8oTCyw5O3+U1Cy7Ex43SlZW74aJD0gpOlOwXPFL+SrSusu/Ef07rbvmmP8gADbH2QfErdOXkjtbhirTiWyWVmtv2Oy6mdyJgM1wO5efgjm6JFWbcuupYs+eNOUTm+7rWMMZL9AM1LfjZrbLER5oii0hO4wOT7FizXanzjPWcw7DQBbrOt1Jyp9uDa6mjB4rBp5UqGPVxegqlT0U6j1amCT64PiGls97OwI9oDITQp0AwzkZy0Hqb4S19yv3tmpHy3N0eLVKH/IdffFPN8JB2LNA4BvNOoKFEBgKwT7Qtxek74bdTyiXHOSoHvpd6HezUkeW/cRqJh9OFgAHB0CxB6qfgWrDdNXzauh7L7y/BipeB887yltNyIVzn5DRbM5LEJwPnmV6TffrYO9AqKrX4qNvBWz8jZ6zXw1DvgEfGM0benWAA/eAvRGYAnWj9Z4FDCbqaYbkB3XMA5dBUh+xYY9H4Hb0KOSWQc7HcKwT7C3RZxAMSkYOG4YupxO6P6VY8crLIDVDIFlTI+acni6QPXEC8sog9xOoKYSaS7WdWV+6tlbX1Nxslch0vGekKiVD/W1Q2FvAXV+v0pUA27aJhV9zjRzO29cbVcSM7Iik2+CwUfloyhQYPVqgWVqqVKdQSGz7oou0z+YaTfimoQsX+MZDYDj0LpZknXUaI1NNjfa/eiUEthgsOaryVu5wAXLPqz4/QwQtNstXSbXZ86Yk3JPDAa7+UFuoRhURY9EUnSlQWNhyUbpqlSqOTZsGuaepFhUOaeF8sh3kMqMxQtSwOwXKxzfBN46p8f0H35JpceKfzsz1bC6s/1kNIf5NxtkHxF1TIqX/0081nk+XopTcSfK1zSnpt+nEqUE0LtvKdQvUy1zQ7rZZFuC1l+bkjDNkW3/7oOxOBmztO6ZdiYbbOwaLdnh0DrGMXad6zpWoGz3WOcVl6XitZX2bHVIM6a42RqGTnKGKw9ocUL4FTqygBWA6EyBuMNTnQV0HVZAyR6ycSl81lP5BHYpa5yu6ElTMYOg9UDS57TXEGnWH5Hre9Hf1qAWVRwwMFADHd4FBXcH2CWz+m/W+dRimdKbul0pCX/YTS76OJELzeAgMgn55EJ4LB97Rc9mDYdwfYC+w9DXwzgOnMYH1vx3G/AZWrIMPDRbsLNNzg38Dn4TELDt2hLz1ynUGcN0MI78ulzDA0P6w9U5wHAHXIKicBm6PmCwIRBMXgGcD+PrC0ckCwLQ0ycRpaUae71uQcgjKJ0N5jiTmhARJ1n6/ADsuDoqelHt6w1WQnKV91dcLUNPTBcKhEBRmQsafZR6r+jac8Avca2oUy/f7dQwQwCfEQfgxgWq4CzRcB8UDxISbmmSqCoclDTudMGMGfPopLPsI3IvBY8R+c66AXb0Ah2TmSy+VrF1To/dsp5H+1bMnXHihFhg1ZeoXu93ohBVJAd9kCPaDQYNhwoTTx2KDQdiyRbHkQ1uiWLLh/3DGq5TmgNuVT/tFR81eK668//2Wz3l6QlNn/YSzAJsWSKay1K0bPP88dOoEGzeqi9WYMWcma9cfbtlx6sgqPT7qFzDyJ/o75JfjefVvVdu75AdfbDHyHz7OPiBuzYhTOitG7PAo1tdcLTbcXt6sM06xOodX7MhX1bIvafSwOwXODpfBtNuRqB1uMeFIOLYRCXR+riQBWExHtOEgDjXHBl2zZGcswLY5tYDw17aV6u0uLUaaa9uyVmec3juzBWP0cCWp8lgkrC9+63PKHiwZ2BmvL+aBxW0XOYUT5G4+EG/EtYxVbnp67CpDjUflkNw5x2Ki5nAnQ+EkKLlXreQ+y4iEoexdSZG751qPh/IlPQf7Qqce0CcTqt6QM9McXS4SAy4YJxPNsp9aDDqSAM1jFT/u1RVSVsPWv+k5bzqM+x0kT4R5b0LtAvC8K1BK6gjnPQmpQ+HVV2WW8b4kNptcBD3/Fz4wGFX/+mNfiwAAIABJREFUYvDMh+1PKu4bdyeMu02vAxmYNnwXHJvB2RGqrtPCIjFRqTwuF4T2Q8LfIWKHilkQnyummZAgZtrcDLlZkPI7Sc7HvgUHK8Uks7LEqOvqBH6pqdDhcXA3wI5rVHmqslLAm5Gh3/X1Aje7HZLfgpTdcGwENAzVefl8AuJAQOzWZrPSo5IcwP1K0/KPVux29Gixt0AARo0SgJeW6nUzZuga5s4F51aIex0IQtYIOHYu1CEGfOWVqvsciag70/z5Wqg4nUp1GjZM+ytfBUvvaWvoChXpvR47Vvs73Th82GCca5X37VpjsXbQ/dT/duh++ZeT09tcA2XvWC7s6LnF3QHoC9V5ug4MsE1MhLvv1uc1bx40HINLrlW44vOMQBMsnCFlaug9LZ+rOwhL7oIjq2HSg6pQ99U443H2AXHXpEjpz7qrBvCpXNOJ+QI2u1OstaHiFKwzQcYhm7ltO/WjbQ7FnG12xZfaY7neDDn6fFWxFwTOeK0OAw2xJeSTcnAVbUHdpsk+1Bwb0OMy9ZJYiwtzAdJ0VAuL1s8lFkoKr9rVNk6dNVDFAeIytdg49GEMY0cOpJbAmFnQebIWBydOwIMPWjJZ67q7dQdVA3bXG23fd08adDpXTRVyBra9nvZGwxHFkDf+PUpGc4B/oMDTViCWVRSGXY9J7jNHv5maTDL6wNENckGfBPF4o8/vUOjUDTofhU2/sRYxw+6FgffAh6tg7dtiwQ6zHOO3YMyvoewwvDoHwkvBa7Tb6zINvDfBSuP9nDgeKh+CPa8qBzbpbph0C7zwgoBr1CjY8gCEFyrlpekOCCTK4GTKzk2NEPc0uPdD42ioGSGw9HiMuHGGWHHKUch6DRqzBebNzQKq+HiBpelAzs6G9EfBUwt7Z4ArU25sh0PyZrnxXSwoMNzOxyB3HvjTwPdNqK0TCPt8YteRiAA7MVGAkJoK9TvB+zeFmJquVJhg6lSlJkUikot9PlhupLZcc42u5/nnIXgQkl5RhbGEXC1c9hrfvfHj9WNK5O++C+vW6bnCQpm5srKMmtTtGLocOQLjkSPbtj6MNRobdYxVq0QMXIbj2mZ83z0pMvv1v02xzy9jhINiqLvf1D0brRjaPRA3FGryYfiNMOECPV69V7HdcF8o+T8Ye+7pvRWxxlP9JcW7U6z+vmbv36bjWkh3uwTOffz0+/pqtBlnHxBHM2J3sgDXlQhEBIx1B9rP0/WmGyDpFAjWHaTdKlgJeYZ72Ne+k9qdIrAJ+dtny950sdLm6tixWU+qBbqxQDvOmCBiAat5/FilM+0uxXAjEbXsa82UU7tqwgr5FXdtXXQkqz8UjFcMvrlGsaFoRzGANw06ToW6XChPgotvENBGD58P7r8f7rnHmsCqPlW91z3z28r/cVnQ5UIY9gPI6Nn2mtsbkTDsXwwbHxajNke4g5F6VAyZ+TBsCCSWwfoHLEnNGQ+DvyOwTMxV/u/yn0XtxwvNo2XqyS2CAYmw83dWmlLXi2H87+FIAObPA/97SiUCyfnnPQm5o2Q0Wr4YvHOtVoYjfwn7OsOOnWJml02DrT+QOzvihbQfwDk3wzPPiBmWlMCBBVD/kHFq98CxRAHKfkNFSEoCX6kKgYQTofYbcmA3NgoEq6sFYIEAxH8A6Rvh2GCoHCLD1ZEjRsnLbKuuc14eJD8K3ioovxH8yWLecXEWuJumLp8PsjIh/gFw1cOJ68CXredDIbF1kw3bjE5NTU0yZ+1/DeLmgs2leLG7QCarN43F0gUXaNvFi/X/FVdoIfDcc1B5CJLmAUb6W/efwFoDVIqKZPYyTUx794oNVhlhpfHjBbROo5b7hkcMQ5ex2PYPkxPem6Ea1kOGfDY5NxyWjL56NezaAc7tBkvea23TcYpk664Xf7mNCCp3WNW9Dn3U8rmC8WKnDRVaANuTYNtLEHcTXPmjUzepiDXWPqgFR3yO1JJ48ydbP/9GDRbOxnH2AXGXxEjpj/KsakWxRkKuANDmgKABuO0ZscyGDeGAQCGmo9muCdrmEODFignb7LrxQCvAWKDqzRDoNlfHXiyYceem421lZJtT5xAJxy4hF99BxdYDjbGNapn99YUI+qByW9sYcEZf1dXNLNZ7Vb5COX2tTVodp0DROfrJHgBbtsKcOZrAPB79djo12Zp/HzoEFw2Bg09LRmu9z4RcTUIlP4CUorbnfqrReBy2zJb56iQDsIF/gJhrOA969YbBxdCwWBW2aoxJMKlQ7LffLC1oKnfCJz9XPjIAbmgepXKU6bkwsieUPwqfGvJwRh+ZUdKHw4IFsGOpQNZhMPsh98DoXyhnd84cOLxGqUn2SrH9KU/D0kNik/HxcNV0+HgWVCwXgGb/FM69Hp5+WiA6cCAEymDfPTJfZd0JezIV67XZJBXn5kL5QUj4q45TdxH4i60qWX6/jmWyUO9fwF0JFVdDbaqA+OhRo/VhrkDZzAFOeAy8x+DETKj2KDZqxn5DIRmEKir02ScmgusDSFkFjQMgeLFl0DJdryYbzsoSOwct5A48YJSazIOqGyCrQEx03jxtc/nlAv53DUXh4ouhVy94+WXYuxvilqpvNECPWbCrN9TUKS59+eVGqVO0EPnwQ/jIAKnMTLHjjh31v69aC8bVvzXuB5c8Af7hkJophl5c/NldvCdOCJDXrIHgEV2jey1gzE1xmWLIxbcqLPRljqYTsPstWPB7cGwHTBOoDezfVGOK4DZwzIGUMXDznDPvifzV+IeNsw+IoxlxcieriEagQbnD7TVVSMgV+yQiIGyP5cZliWmHg5K/YzqMk7WvSEjyeKwUqvhsxYWba2NL4nGZWgC0V5UrIU/ydXN17JKaaT0U4/VVxqi37IAOw+UmDzSoxFxr5pneW8CbN0LbH1mtZuitO61k9YeO56hFXP6Y2IaLUEiTcjCoyc38XVEK2x6Co8sh2OpzSSqE7ldIzk08w7qvkYhW+BseiQJNgBzwDYZAf1U8GjYM+hbB7qdh7Z8sdpM9GIZ9T6Xz7E6o3qNiAVtmG/txGAA8Uu36xo1QT+LVhnPZnQRj/leT5roN8M4CsC0Bj8HS0nup80veCMUlX38dIqViekTkMC35M7z+gYCoQwe4dCosuBQqNyoNKv9/4LxrYPZsxUL79IGcBFh1DdjroMNV8GlvgUCfPjILpacLoPhQsncoD8J3gi9qUef3W2UkvT5IewhCHqj/HlRWWWlFTU0C6tpafZ6ZmRD3BMQdgbpZcNhgmrm5Al+nU6am+nr9rqqCeB9kPwZhp/YfdohpO53ap1ksJBQS+O3fLxZOEOp/q1aFziFQdaFaCvbqBW+9pddcc42u1fz//PNh6FDFgNeuVdw4/jV9R/PHge0G2GZ8T0aPFoiajPbIETHuQ8YCd+hQOa9NQ1lrQ5ctDRonytCV00E5yN27f3ZA9vuV/71qFVQc0rm614AjyhfR+QLFkrtccOoc+DMdhw5BYy1Ur4X9r8Px1XDVemvxHKyFJd+WA/qC51SX+avxLx9nHxB3jo+Ufje+/WIdZv9gu1PpOLX7YqcAOeMM+dml7erbyS1O6CDpO+hrf5vEPIGu2XSi9fCma8EQao69D0+q2HQ4KBm5dS5yXKaMPtiMrlGtFhGeFMgZpuP4ayWZto6fp/UQ8BaMl6R8dJ2A98CSltvFZysuWzRVTe/PtDj6/iVKCTm4tG3VsJQuRlOF736+Vmm+Ktj6tAC4cpv1eKC/Yr+hQigoFADnuWD9n8WUzdH5fB3b7KhTu195i5seNTawQ/NICIwCVyqMGwvJn8Ky+6yFzKBvwcj/hoawJu8DKw0WbHwmJffByJ8CTjG2VcvBYzQTABhyF2TfDHNeF0Pt2RPOHQFzzoG63RDKgc6/hvOuFAifOCEH8KD+sOAicByEtBFQfj4EwjBihJVP3KUL7N0MiX8C/NB4MwQKrMYNkYgWSJGIkTa0GtLeh8ZeELzKYqUZGZKvvV4Bpt8v1u2ZDfGHtN/DBrONdkPX1Wnf6ekC8vh4vca9D+qmQWRQWzbcoYOA0Cx/WVkJgwfDpo/A8xew+YCLoG6IrjU52WLCN92kY7/+uv4305Y++UTb2I9C6utqgpGYDz3/D5bu0jkWFEjWNms5h8MCxnff1d8JCVaqkznKVxkVugwGbesIDZNkhOrYUcc32fRnGZGIFh+rV8PmzTpfVym4N+jzA80t/W+XahNda3nV/2le+CJt/Db+XeGci0zHeMTqZ77lKfjoPlWwGvrd/6gqVmfjOPuA2GTEcVmW+SjULIbb1E66UVKh4qmRkIAyVjzX5hDYOT1G/LidEphJRdrGXxfbLOZONiTqiApbBGOUsEztrqYQzdWxj5PeSzJ20CcJvrUpLKlQ1W7cydpHxdq2AJ/aTYBTOEHHO7ZB7f7K3m61P5vYbtFUyc2Z/c48YX73AuX5Hl7WSnK3aQHQe4aKYHzWNmjRIxKRTL7xEU0OJ3edA00DIDAAiJdsW1ICkTItBHa9YW3b90ZNJpn99H/dIUmO6x+ytvGPkFuXJE3mXV2w/F4rjlw0FSbeD6k94eOPYfEicH9kterLLFYsOGeIwPOVV6BiO8S9Iqna4Ybzn4XjeTIfgeTWYV3gxQnQdFhtGnv+DqZeLDm6vFyx36lT4fmLwbkOvIXgvBvKq9X4oLxcx+vXT5O5dyG4VkGgDyTcoefi4gSMdrtAJhQSELtfUPvAqguguY+e9/vFaCsrjbKZHr02JQWcT0PCPmi8AY6nikHZ7QL3lBSxZ48hWYfDAlfHekiYB6Eu0Hi9dS6JiQJum82Spvv0kYIAShv66EmIf1r/N90EwSKBY22tJGWnE26+WWD88svabtw4xXB37NBj4QbIfBuaDSPcqL/AmoiMZi4XXHZZS7Ctrhar/tQIffXurbh0UpJ1P+6aaxi6zFBIX6ifCBGjNvakSWfuQK6rk2S9ejU0VIFzC3jXgS1qfuh2iUA5vSc8O1SEo8t0GPd/nw8ol34P1v2Zk3X2w0H97XArRGZ36Tt707avZOp/8Tj7gLiTN1L6rXbivd4MoyqWW7HSurK2BcVB7DShg27e5prYYGizy6jk9Iox1+1ru43Dq7QTu0sMPRYwJ3XUyjUcUGyytdPZlQSZfZRn21wtwGxd0zmjr1zL7kQ1I69Y1TapPqWLBbw5Q2SI2rdIrLdqZ8ttswdZwJs/2ugUdQYjHJaRaf1fBFQt5HubzrffTTDwzjPftzmaa2HbczJfRbuzQ8XQPFgsJCVV4DugP5S/B6t/Z1W5cnrVgnDQty0m0VABq34Dax+w9hccDr7REEmSJDm0O6z9JWx7Vs+ndoMJ98tAdvCgUct4vcGCjQXdyJ+JOTjcys2cOxfYDvGvAs16Py56BZbttNy606ZBRze8OB78VSrlWfwHmHKBjEf79oktXnklPDUTIvPA5oUuf4b1hwReHTtq8s7NFfid2KrYMEDoXvAbqUKmGcrlshgxIUj6rcpLHv8W+I24blOTwPLECYFkWppMWYmJ4HgOEnZD47VQ3UH7rTUWdWaRDq9Xv10u/XZGIO0BHaf2m0C6wNrvF1hVVCi9aK8Rtx80SO+ReX2b/izjmysFqmaq5vL11wtoV63Svm65RVL480aYYsQIOPdcMe3nnoP6WkhbCUGDSQ/8FtRNgPXGfVVSosWOKZVHIlrUzJ8v45nLpf0NGWItUkMBLQ4//pG1sA2NhKbRSm8bMEALgs/aPenk/R2yGk7s2wf28iiWHLLu7QFfh+E/gnmXSxG74LkzX+iGAiIdDpcFvP+BVav+HcbZB8QmI07racR8wzIi1OyJ/QKzFjUYvYpjSMN2t/KRnXEC3ZoYhUJsdisu66+PbRbzpAgQHR6dU6xt0npCckftr6E8dm3X3OECXlc8NBwVuLS+vuQiA3gnKnbbeNQC3tZdVhJyodN5hslqyudrfRYOi5FufFh5tdHyuc2hMnfFt0D/W79YTKtijaTnzU9YCxJHFjT2V+GMSIIMPcOGQecC2PaMCn+Y7CQxTyap4lvUZxpk6Cr9HZT+3ornR4ZDw0gVcOjXD8aOgD1Pwif/rW0cHhjzK0nRwYgcz6uWg3uJVQEre5BiwdkDBCwLF8K6NeBeajHl3jNgzP3w2ltQVqZJ/ZprIO4YvDQJQo1qYj/sfhg/GV56SWwsPR1uuAFe+m+o/5P2NeQRWHJYLPTCCyWN22xqeLBiBSS/ApGtim/n3qKJPD1d7Nbl0jme/M7ugZTnIJgLTbcJoF0uAY/TKUCORCQFm+BsewESd0LTVVDXSY/V1Yk5O526R7xeq8a1ycDjF0gG5xyoG2Ux4MxMAX4kovjv9u0qNOHzCURHjNA1VD0Aru2Q2BfKLwV3HNx2m1jxxo1aJMyaJTb7zDM65pAheo/q65X2VV4O8bvA+ZJCVYUTofNPYOFH2t5c9ES7hRsbJVWvN5pvFBVpAZWZaW3T2tBlc6vVZfNwwKnPZtw4y1F+Rt+FCgHyunUQblIHqLj14KiHW/dDfLIc3otuV7P7S9+EpFOU5/xq/NuOsw+Ii9yR0m/HcCTb7AK5aKNVLHexK8FgunEQrFe+YKwGB2k9Bawhv9hnzFZ9/RTrDPpVqLx1QQu7EzqUCPhCAZmCWncWsjnEYrMGimE3HBKQtq4allgAHSdZrDcStoC37J2W8Vi7MyrOe46k7s+z0g0H1VBh82NaMLRozOAS8x7wdYHN58k9NIe/Hra/KJCvWGM9busPDf0la7rcmlyHDYO4iGTltQ9YObxZAwwD1lVWqoSvSiC9+reWi91WAnUjIJKm2OukSVC/HJbcbS3Sim+FMb9UvHzHDhmCGrbKbGU3vAljfqWKWw6XXMYvvwwn9qtdn8PIQZ3yN8i/QkytslLs8rrroGEDvHqeACEwEMY8AKPGwmuviYklJcHMmbDoWdh/t2pPD/4FLLOJ+V54ISxbJuAZM0YgHNkO8c9BJA68v4C6gBipyTpNQDZjs/FLwLEUAuPBN8FKJTKrcnm9Amev1zJ42edAwhZougwaexotDf0CcLMfsJmi5nDoJxSCuKPg/JuqqdV9S5+l261jdeumClqdOkkurq+XLL1kifZz+eUw72VwGy7w5PPhUImuZ+ZMLUZ27NB7O3Om3pOnn9a5FxerulYwqDjytm3gOAoZ86DpkL5TE2bD4k8F/A6HGkcUF7e8P3fv1nGqjXtt4sS21ahqysSOTfOgMwPqxqlftcOp1KjOdkjKkbR8JsPn02Jg1Sqoe08pUIEbrO9DRobu8XUPwiVz9b38avx/Nc4+IC60RUrvyxQjdMZbJqpYsrAnTWkAzjhJ1TV7YhfhSO2uSZeIYs2x2HVyJ0uGbjqubj+xtsnsJ3OXvwaObWrLwD0pUDBBbkS7S5L3gQ+NGspRIyEXOk4W6BZO1LUcXGIA77ttz7HDMAt480ZKJv08I+hTTuDWpwwHdXRdZ4/c2IO/Bd0u+2LgCwL3DY+oopUpbzszBL6BQZKLc3IkHRYXQ8N+WHM/bPibdV5FUxX/LZpiLTaaawXSq35jxaydJVBdojhefr6MNfHVsPg7lvmmYBxMeAByBgkQFi6ELevB8wG4DUNUhxLViM7sKya3dq2A2nYAEudApEbGoItfh6ZMsTG/X2zq6qvh8CKYe4n25R8Ok/8Ew0q0jzVrBHy33AKbV8HqGWCvgm7XQ/kogcXgwXrfS0u1z8RE2LIJ0p5UUQvfhdD9BsVazUIbNpskXJ9PzKyhQRW37OXguwX8eQIrk8maTRnMxhFmTNk+FxLWQ9N08BVbUi5YTNsE9GhWHAlD4iOGGembUJkh4C0rU35yVZVY98iRMlolJAhkPvxQgDthArzxCMQ/ArYQxM+CigJJ2l/7mt7jsjI5rm++WYA5e7YWIr17C8wdDqkaH38MNEH+YqhdDdjg3NmwL0PxWZA8fv75LQt3BAJaHCwz1JCsLKU6FbbqRHRkNSy5x7qnPF2hagyEMyDhb+BJgGuXQUaPM/226D19ehTUVkNdOhCnhVd2Z+gzBCK75dU4/2mVZP1q/H8zzj4gLnJFSr8dwwUdny2ma1asqimLbd5K6aKVsN2h1J9jm2hT1MOVKIblTTUMU3vEeFuP3BHan90lAD+ysm2pyKSOmuCzB4q1V34qQI12/Zrn33GyJTcndVT8dd8i/Zixz+j9djpXwNtx0hdrlu2vV37ttufaxpOdcZK+h9wl1/EXGU1N8PabkHkIDrzS8ppcA6CmD4S6AXbJxcOGKU54ZJXiv2b+LkCf6yVBR3e48deLFaz8tRWLdw+DqmGqu5uZqVSTwjRY/hPVngaZ3yb8UWUHQVLg229DaCfEzQOboYaM+53eB7tDk/ybb8LmTeBaLZMUKARwwbOwbZ+V9zpwoExGO1+AhTfosebxcP79mvTfe08A4XRKYq06Dm9erKIPGSWQeR+UrteiZMIEydcOh5jxvHky9bjmqf9x1q/h2ImWbDM/X2kryckyNrkaIe73EPFA7Xd1+5vszmazgNSUlk/eCwsgbjU0XaAiKXa7tY0Zf/Z49N6Ypqxko6Vi2kYIvq4FUdX5YrBmFS8zLpybq9ft2aPF1+HDissPH65zKn0c4uboe2S7G2oSrK5KzzyjaywokKRfXQ1PPaVFR7duWgS5XDrO3LlAGAo2Q43huB5yF2TeBHPf1HVkZUmqzs5ueQ+Xl+s9NyuJlZTonvJElauMZeiyp0FTH4VCvCthzIswbNKZL2aPrlfN86pDsG8bHNkD4XpV7HI2gzsEGd3hWiM85ffrPh0xQvfBV+Pfcpx9QFxoi5T+uMBguvGqc1pXFttwlVRoxH4TVLKxelfs/OGsgUYnIQc0HpM82rqpQVyWmGZCriTbmj3qvhPLWFUwVvu02QT0B5e06piCDFwngXeCWHn1rpZyc7QJyuGx4rydpspE9EWMFU2VArcdL7VdZLgSleZUcq8WEV/G2LsC5t4HoU84WcDAmaaWgw3FmqASEgS+Q4ZAYoIKEJT+3mIXDreMNoO/07InaqBRLHnFL62FkHconBgK4RxJvZMmQb/eMpgt+7HeW5sDRv1cPYVdhkHpzTehbKcMQm6DIeWPgamPQ7rBYg4fliu6qgLi54PDdOT+Qqat9z+wmJOZUrPuL7D423rMdy5c8gc1pP/4YwGxzaZ0HI8HZl8s57OnA4x6Gea9L6C8+WaBcF2dzEOlpXDiEKT+FUJ10DgDhlwjCbOwUJK036+/DxywSmCm7YLgc8BAqLvYAk2v1+jYZICpKT2bErPrPfAug8ZzIDCiZU6w+VpT+k5JEehnZOh9zXCD/0eqm+34FdQ06/q3bBGzramRdD5lit4PEBDOmSNgmzFD1bSOPyF1IqEQjl8PQZd6FffvD08+qdhzly5w7bVaAJh52J06WSUxy8rEopuboUMFND6q73HHSTDmEXhrsUDdZlNMeNCglt+1cFjhALP0ZlKSFlo9W0nOpqFr2Y+1aB/0ACxZDkeeNfKc74Ep0/S6z/tdDgT0Hq5apc/WHAMGaJFw6JCUlro6FT5pfY5fjX+LcfYBcXuu6bgsVToyGyfU7W9bnAIkL2f01XbBRoFfa5AEAWnOYKU9+evkZq5Y3Xa73OGQP1bGnXBQRqYDi9uasLxpqkplSs3pvRTD3P++JTe3bnSQO9JILTpHkugXLRNXfwRWG00VWkvm7hTJu8O+D7nDvthxzBFshk9fg9V/gmMrrccjPcA3EII9AIck1mHDJCNGArDVMGCZcn18jipg9b9N0v7J/fuUC7nif6z87fghKtcYztOkO3689r3/bRWfN2sI97leRTmS8gUyy5dLunTsgfg3gWoB9YQ/wqBvioVFIprwFi4E+zFIeh3C5Tqni16GvAmK827fron1yit1TSt+Cct/quM2XQxX/VbdcEpLrYIU110nRvjIjcBrqqQ2fTG8uERAd/nlYrcbNii23bGjgCl9OQQWQbA7dP21zE11dRbLNAtlgNjd0aOQ+haE1oBrBlR2lbO3utpir6Z8bYKryXbdS8GzRMUsmkcJhE1GbIJ3fLxYrgnIZjpTKKSc3tBGSJkJBwsFmOXlWgSMHasKV6mpUkM+/lgLiD591MYwJUXg+vjfwfG4OlnlTIBd4wCb3r+cHHjiCV1Lr15w1VV6L556SiBfUKDtTFf488/rd0ojxL0IDQeklk1/HTZV6p6wVUOfYTD9ipasFySpv/WWYsighcX55+vaT97rYXhuOAz+tu65SERmvIW3g28PNM2Awi5agBSdYVW56BGJCHRXr9Y9Yg6HQwqB0wkvvqj3uaTk8x/nq/EvGWcfEBfaIqXfS5QhIS6Lk3HditK2VbCcXoFZYoHhUja2a10MxJUg5pfeR6zLlJlbA7lprDKBN9QseXX/4rYxY09KS6k5o48MQ4c/EfDuW6R4UvRI7WrFeQsnShr/oqNmn1ydu+a2LQTizYDO56kIRWbfL34sc1R9KoDc9KhVw9qVAoO+LiPU8TA8+6yYb0mJJtCmSrHaNfdbn09mP8V/e13TMuYd8stV/ckvLG9AwmA4OhDCRu/VMWPUHKF+twB4n5G7mztcceC8Efr/0CFJjRX71CXJbTYDmAhTH4PULvq/qUmS5vbt4NwM8XNltsodLhAm1XLnJiRYwLr0u5L9AXxXwzW/FgBt2mR1UrriCjGVx34Ajca2F86BxUfFaocOlbz64osCxRkzxPQ4AYkPavuGO2HcFYpjFhQIQI8ft/KLi4oE0m4HuH8FtmZw/RIqA5aRywRksziHCcgmyHo/Ade7qrnsG2fFhaPlbDAqNAUtVmxK4wU1UPMAODpDwyyB+9ChWpB07y4AP3RIoFRaqnOZNk3vVVmZ7pcePeDFRyH+YbUZ7HgrbMkT0Nx2m34//rjOe+BAscD6ehm4jh3TvXbDDbq2piajLOZecAWgcCkcWwbYFF6oc8OH10KwF8TNErC37t8bici5vWDyHXlrAAAgAElEQVSBpSKcd57FovcuhHmXwfg/aM7KLFb4LByCF6bDkTKouwxw6D2YPFkO7i8yGhrkXVi5UvfVNKPjUVWV0rm6d1e61lepSv824+wD4m4pkdJ7U9uyR1BcN6Of0lYC9Sp6bhZkiB5pPSUzp3TWF6J6l+TP1vK2J7Ul8Ppr1bru4JKW7l6QnFs0xZKaM/sBNqjcbgFv2Tst036c8Yq7mrWbzUn/i44TOxQnLVvQttJXfLa6/ZTcB2ldv5zjgWS43XPVcrBFj9RuMOoeKJlpgWlDgzoyffvbEKgQ+K7/qyXzd5wsAO50bsvJIhRQZa1Pfm59VokDJEH7jbSNkhKlizj8atyw/i/WdY//PfS+Tosyvx8++EASo+NTSJgvo5XDrfrR/W/jZHPyAwckRddWQcIHYDe6/wz8Jkz4A1Qc1wTX0KBJ9NprJa0vus1Iw7KB/waY8Qsx1J07rZzXadNkwHrxITj0XQHkiF9A5UBJiub+Hn5YQHXxxXL/7twJuYvk+PaXwKCf6/GaGotdZmQIGMrLxcy3bYO8ANT9GsiHult0DibgmozYBOKTDmuD5cavAcdbEBoPjRMsSdt83ny9mZ5UUKAYb5cuivsW5EL13WBrhPz7YXu1rn3zZn0eF16o3F2vV1LvnDn6+/rrxXRDIS1C9uyBFS9BwhM6//yfqc9DSorAuKEBHntM+xw+XMDY1KQ4cnm5vAI33KDzDYWsspiEoXcZHHxG+3Unw+g/wtL7oH4KhHqI8ZaUtAWxhgYx942GEtapkz7bJDdseVqV7I6u1XyQ0kXzSWax7s+4vnB4HDQZRKK4WM7s9M9RfS56zJ6txUu0C7ypSeGNuDgVM3F9QZXtq/FPGWcfEJt5xIl5kmuTClHpx8NisW3qLtvFdjsM12QcqFclqoNL2zdWFYxVPeLGo9ruwOK27NUZbwDvBIFvVn8dq/EY7HvPiPW+YzWhN0f+WCvOmzP0yysdV7FetZDL3m2bapWYD90uhZLvf/l5hjVlYr4b/26BvjsJkqbC8a4wbaaV3tLYaP3e9i7kbIdji6x99bpGAJwzuOUxwiGlhSz/b8stnlQM1cOhMQ+wKUY4cSKkJGkx8NF9lmFr+I/UUMIsePDpp4oF11aA9x1wGVJe0VSY+qjyvEFsZ9kyI4ZbC6nzILhb6WHnPQ29rxG4vfyytu3Z03DoAvOvg0/nqEdwcCbc8FPFaMvKJJVGIjIZjR4NHyyA0hvBcRy6Xgmdf6R0G6cTvv51LRi2bBEbHDTImEjLwfl3iLghcK/a2r3zjo6RkKBrLCmRlJ6QILZ76BDkboD6NyDuQjg61JKrzaIfkUhbefnk701gew0YB3UTLQadmSn2bZarNGPSZqGOvDwx+1AIckuhfj6kXQL7B+gaS0okA/fuLZl7xw4pGidO6P0dPFj7eOstncsdd+g9OPKqUUksERJ/BvvrtdC54Qadx5NP6pgTJujH59OC6cABnfuNN8o0FolYZTEBetbA4Qfg6qWaD8reg3nXQeVMwCPZ+2Ijtt567Nqle6vGUIImT5YyY5rhQn44vkWgXLFWAF25Da5dA5sPyikeNBbrw4YptBItdX/WUVcHf/iDvhdJSboH4uP12+PRPRUMKm7+eXKcvxr/1HH2AXGv3EjpX69UUfKDH7ZtuJBUqKL6HYbIpFV/GMqXw4Gl7Rur8sdKNqrdJ9A9sBjKV7bc1ultGePNGiAQDfrUA9RkvUfXtXxdWg9N8J2m6rXupC/vzTi0TIarAx+0bXaRXKSc2mH3Qnxm7Nd/3hEOqoXhxkckvZkjfwwMuAPSJ8Ajj+uLb3754+MhPg6Cm+HYK1CzVq+xO8Ush/yXzjl6RMKw42UBsBkvTu6rohC1uYCtpZxXtgiW/JcVUuhxJYz7rdXJpqFBbuhNm5SLGb8AInVyhk/6C/S72WI6DQ0Cw127FDdOeh1C9VJTLn5NTTNMkAZNtlOmyOQ39zItwiJxEL4NbvqhAO/wYTG7YFCsdfJk2LwR5l8Bzk8hbQBc8CY8OlsAcuWVAok5czR53nabJNaaash7Beq2yfg14Sdiz5WVMnG9844WP/376/GBA5WH6nZD/N8htA8yfgJldoutmqlOJrianbN8PovppuyE8AtgHwM1k60cZZP5mvHoaAA+ckTg2r27FgfFWVD2TSABch6CXXsFkh9/rPflqqu0sLHZZE6bPVuvnzVLsvvu3TIiTZoEf30IbC+BayNkDoDqGVBVD/37wqVX6ByeNkpknneenMN+v0IIe/cK4G66ySrQsWMHvPQCuF+E5A4w822r8cM7t0BDM+wqttj/lVe2TV8CHWPxYoE76H2aPr1917KZ6gXa98cfWz2XbTYtSkaPts7ls47du7UgiF4ANzS0/HvyZKWNfTXO6nH2AXF09yVQjC5vlGSeSEST8KGPYkvSuSMEuvljJA1V7TCAdwkcXt5yW4e7pas5e5BAIxKRueuk3PwuLXJt3ckt5WaTXX1ZY9/7chIf/LBty8bUbmKVQ+7+cuLLrUfdQaX8bPy7FZt1xhkVtW5vGWeOnlyCzUqNKv29lbYVl6XzHHC7jGzRIxKBXa9LWjaNdMm9VHjiRDZg0wRoGlyqPlUsdreRLpQ1QPJy4Xhrfxs2yGTlr4K4dyync5eLYMrDLQvq790r8Guoh6RVwNt6vMdVcO5j4IgXOzPLVU6fLtbmq4bXLpBvIJwE9m/ATd+TRHzsmGKXPp+YzgUXCJifvhrcy8CdAdevheffEkM12dCDDyr2eMUVAr2PPoIOB6DhCQing+MHMHGK4tc5OXo/Vq3S6zdvFss1G0P0zIfDt4mlZz4MZfvFsnfutADZjOeacWO7XYyqpgbS90PgSXCOgqpz2jJf83d+vq4tErEeGzxY8m/nznDiZxDZB91/BWv9OlafPgKg4mItGNasEfvPzJQ7uUMH5Qw/9JBiy1/7mljmc7Mh/jEV6uh2DWyzg/NV6PwNuPwPium/+KI+p4sv1j6DQYH9zp1itTfdZNWG3r0GXh8GwQGQeA7M+KEWJ74qeKofTHoSPjmi9wqkaowaFTveeviw/AdHDG/GiBFaQETnJ7c3amq08DDvMbdbC5Zhw748OTk6xv/VOKvHqYD4S+zNdQbDkwJjfyhjk79WzLXsHcUZo4fdqcIZJuPN7A/HNwh0S3/XtgykzSGpuWACdJwohmyWamw4ohZoZpy3dUvBwomW3Jw9yIotfhkjHFZj73V/ktGrRVqVTe7rPjeoprI7RovCL3z8kBYdGx62gA60AOp/B/S8KnZrRJtNk9eGR2RWMhttZPQxDFjXqnlG9IhEYM9bAmBTWUjuDqEpcChL15udrVV8jx5SAZbeq88TFNMf91voN9OS/CsrBZp79qiQfvJCNQJwJaryVe/rrIkoHJY0uGQJ0ASZ70KzYcKb+CeVu2xqguefkcTsdkva69xZ98QrU3WPhdPB9S246b8shvnUUwLh4mKBcF0dPH+PQBg7XPk2LF0nEM7NlZlmzhyBcN++uu45cwA/hN7UOfmmwvSpRpEKNNHPn6+/zQ5IBQVRaS2GquAZAIePWO85WOBgsi5Tdo2PFzsHpdAFAHu45WtM2dXMOT56VMc9cEBxWxB42u0C5Z4Xw+E/w6E3IOtGq9yl3S614qabBEDr1kkFyMoSmO3Yodjx669r4fHNb8KYibCsTgVDdr0AKflQNQp2vwjbb5WMfOml1mu8XkngV18th/uWLVog3XijFhBdh8B1W2DOfdD0ODz2JAy4BUbcCZMehI++DdevgxWlctkvWqRruvTSthJvXh7cequY8XvvaTG0datix2ZP5PZGSooWDqNGSUbetk3S+fLlAvOBA794QZ2vAPj/i/GvAWKbQ0Ub2lSsijJWFYyFtF5wdI2A95P/FoNssR97y8pVOUOt9KBAowxHZUZO7/FNLV+b0dcC3oJxcl1/mSMcVn7v+ocUmw5HleC02WUE6ztT5SWdn7OC1ulGwxEZjTY8bMXd7S61Xet/+6n7lNbugzUPyIhimtMKJwiAO5/fdqESieh9XvZTS8lI6gKO8+FAOmCXFDh5smE8icCmx+Gj71u9nIfcAyN/YqU3hcPWBEgdJL0LbFLxiu6XweSHWrZ4rKuTi7msDOyHIW0eNFdom2mvQv4oxSyfe65lucrMTKg9AC9PUo3yUAeI/w7ceKeYZH29QLi+XouHSy4RKD37K7C/pGNf+BwccQp4XC5Jnlu2CHji4wXcc+Zo26774egxCHaGrPGSj00g8/nE9nr00HWA/v7gA+231vA5pI+CE36Be6Xx/pmTcmtA9nolYYKAGFTdCqzKWuZra2utvOG0NAGxuU1ZmWLo27ZBzrlw6EFoXA1DfwqLjwmAhw/XZ7Z+veTYDz+UxHvhhZKoFy2Swc+sSz1/vmLye0uhKhnSJ8ENj8OGLbBkCrzyV7jlPknZPp8UkZdekvmra1e91uXS8Z58Uo8XFUFub7jjFd0POxfBmkWw7a+QN1y+kpW/grG/1LavvKLwxV//qs+tU6eW97bDoWvp00ex4717dQ/16yfj1+nis1lZWjQcPCjg37tXLHvZMn0fevf+ClD/w8e/Boh9lVBf2dJYlT9WVbUqVktq/vD7+t16mLWaCyZAbonl4o2E4egGS25u4fpFTSM6nSfg7TilpYz5ZY1wEDbPVtz16PqWPZRtTgFf/9vV1ejLbBQePSJh2P+BzmHnHOvx7EGK/fa65tQx7op1YqdmA3Uw4tTfgw4xVRVY+gSs/TWEjVzMxCKImw57UgG7gGDiRLk/nU651hd/x2LMXS5SaohZbAOiJMFycG6ChLdVNN+TCuc8othx9OS1a5eAztcEydsg8orawXacDBc+L5Pf3r1ty1XGx0PlTnh5IjQchmBHSLkLrr/VSo955hmljXTqpInabocXHoaGv4AdGHafAOThh3Uul16qydtkttOni83v3QtJIThmyKzNUyWLmi0Vx46FpUv1d3GxQMSsfAXQszvs+5X+Ti0BPhVjW7/eyhMGCzjNnFmvV4sUsDpp2YIttw2FdJyqKgHDiRMWkFdXWzJ3To6A+HAlxI0E33I48S54chXPNOtmr18vQ9bq1YorjxolMN2wQdd70UUC9q1bdbym/wUGwMFesH4rlAyHzZOhfKPc6bfdJpD3+QTszz2n+HNhoViny6VjzZ4tV3bXrnrs6qvhgyz4qBB8ASh0QpZdLTZHGw74r38d3nhDMvfs2ZKPx41ry1bNJh4bNijVafNmXdv55+vaTgemZsWwPXu0uCwvl7xulmvt3FnbzZ1rVV37CqD/I8a/BohTOsOtSyEhR2zxwGL44FttwRMstls4Qa7paCm07qBVPrLsbcmo0aPjFKuYhumI/rJH0K/c2S1PKBYabTyzu1U/euCd0PPqLy5DnWo0HoMtswXAZsELmx363qwYbs7Q9r/UkYjk+tLfW5+Bza7zHnKXPq9Y4+DH8N534YRhinNmQNZ1sDMZMBoGjB0rI4nHI5a99F7YafSdTe8FEx9QipM5/H7JysuXy+Wc8h6EDRbc82sw6c8tO0+FQmKLy5YBAejwMTQYysnwH6nqlt2h2GZ0ucpp03R+R9eLCTdXQbAbZNwFM2ZajRKee05x3bw8SdguF7z7Fhz+JTgaoegiGP5TePQxMfjhwwUszz4rYBwwQAD+5z/r2Hnr4XAI/IOgyxix3yNHxD49HoFdVpbl2O3Xz+qrm1QLNAG50GAoP/FGSCEvz2LGpswczYxNF+/JlpbG/+Y9WVen41ZUtGV4+/bpOiorLd/Arl0wegZsXA77X4UB98O62bAuTzHQVasEjBMnCrQWLdL7t3WrmPOgQfoMXnlFYYex98K6P0AgARYg0Jr6fXjlcqiuVYz4ppsEkD6fWPczz8gAlpMjxcHt1n3wzDM6llntavJksfw33oANKK3t2gut+SA+XtuvXCkj4JIlWiRcfrnVw9gcNpvun27dtO3mzdrvxo1aXJwuXclm0yKhSxe9F++/r3j+U0/pcVMJSUoS+z///K/A+D9g/GuAOOSHd2dp0m/tmC4YZ8V4c0e07IXrr4c971kGq9a1nrP6R/XoHfuPa4Ttb1Qz7q1PK6ewRVMFr/KbB30Huk77x4JvJCK5fuMjLRlsZj/FfvvMaFnFqvUI+fW60t9bhipvumHAuqP92tflKyVB7zNSRbxZMOyH8HEAdhoS6IgRAuGEBNUNX/YrVc8ChQHG/K+OEV1pbPdugWVNNTjXQ8I7EG5WKdFzHoXul7Q8j+pqseCDB8F2AnIWQsNu7f+il9R/OBy24nJglau02eRYnzNVhrlAX+hwF1x7vSb0YFCT/8GDkoxnzBBQrl8Pa78PriOQ0humPQ8LFir1Jz9fceE1a3QtiYmaSBcvlsO1yAaH34KIE/yTdC5vGrHisWOthgVmyhJoYp4zR8y1yriGtBGSjMEC3awso/et3QJd0xDk9VqM13y/TWnavD9rawUEFRUWkz5xwnJVmz159+8XwG3fDkl95SoPHYZPZ4HbAzvq4OZXdP5r1sB3viNwOnxYAHPOOQLm+fPFRM1iJft7wLXL4ZUroGYbvBSEO34MCV5wNAus5s4VOE6dKjBet04ANmuWgHbKFH12ixdL+bjiCu0fBJ5paWLXGzfq3rn6amvRYbPpni0s1OKgrEymsiuuEOi2HomJem7AAH2Ge/bIlGc6mKO7OsUaNpt8A7166ToWL9Y9s3evzquoSG7x997TdX0Fxv9fj38NENcfgn2H9HfeaIFuoQG80aahcEiM2QTeg0tb7ic+R2zKlJsTcv5x5+yrhTW/F3C1bm/oShDwD7kbOp3zjzsHczRVahGw8RFjIWCMPtcLgPNGnvqL21wj1/SaP1p1u9N6Kv7bZ0bLxU/0qFirMo97DMk1Eg+Dvgfjf6DXJG7VKn7WLE3ckYic1kvusdpLDrxTLDUa5BsbxS42bgRbDaS/B4HNYsF9boAJ96tVZfTYtk1GnUAA0g5C+FmlpmQPhulzxOL9/pblKq+6SmwVdD+9doHS4fyDoPAuuPprAq9wWLLwnj0y3Nxwg1jT/v2w4C7wbAVnMly1ELYaJSvdbsnWtbV6D0Cx5KoqMS0i4DQe94+DAWMUtzUbOeTlaRHi8VgO7dRUq6Vh795wcLb+zp8C+4/q3OqNPGsTULKyrMdM2dlkxk6nFoqgMqQg0I5u7gAWOJeXKy5aYXx2NpuAYvp02D0blv8OEntDxWgYdS7sexmObdf7NmSIgHjFCgHJyy+L/X3jGwKe8nKx2gsu0PY7d+oab1kHj94I9ffDcweh19egsRbWpQqwMzMlHU+bJhPc1q0C41tu0fmPH2+oFu9qARMIiH2DwO3226Vy7N8Pjz4qj0BWlMKSny9J/c03FeN/9lnJ7RMnxgbX7t3hzjulyqxcKeDc/P/Yu+74KMt0e2YmnfRGGgkkBAKhhlAD0hGp0pt0EMG6Va93y72uu667uqvuKgJSRDpKr0oNvbeQ0JJAeiW9Z+a7f5x57/vNpIMKq/P8fvwgk5mvDt95z/Oc5zwxvEZ+fjXfbx46HZ3JOnfmd9XGRnpJC/c1GxuelyV+svFkgLiZDzBhLcUz5iKpwgdSYHX/oNnIQ40E3qChFFz9kCvF0hzOCL2zhcelDhsnoMUg1k79o364YxChKED6WQqvYtfK193aMvXcfnZNsDKPwmTg8sfA1X/J+c3+/QjAIaPqTt1n36AK+p5xyo21M1DRDxjzV6BtB/m+Nm34AMzPB8rusA6cbhw9GDiYaWhP1fuFteD+/azt2l0FbPbz4dnMh0MagkeYHkt1Nfdx/jwAPRBwAyjYyd91epHKaCs7AuKGDUz7CrtK8WC88w2weyL/XdkbCH6d7Ean4zHt2kWgd3CgEtfZmee08W36NAPAhL1AmZ1Md48fT2Bcs4bss1s3MsyVK43HpgCJ5wGDM1DVm2CybRt/168f7SABPpRjjT3UXbrwOAAgyAu4H0827doFwLcEFjFBSLBfDw/ZaiOAQzBcna5malr0GIuBEYCpw5boz01PZzo1Pp770lQB1a7AoK+ADVuAG7eBzm2A7BgC0qxZBOLz5wlkok/58mWmcFesIHh17Mga78aNZMrBwcALy4DP/IHcLcDVMsDGGph2Elj9JdPGnp5kuuPHE4zj48ke587lve7Th+C1Zw9ZtHDnAsjOFywg601IAJYvZxtViMqhzs6O34dWrbiNkyeZbZgwQWYG1GFry8xHx46y1Wn5cjLjgQMb1+qkKLw+U6fK1xwceB1Xr+Y2LL3CP9l4MkDs6C+ZY0Uha8RiYlHeXdP3ekdI4PWLqtku831HUQpw/n2CTnGq6e9s3Xgs3d8CmtejOP4+o6KArPLa56bK77ZTCcAB/RtejGRdY/o5bp18LXQCFxG+Pev+XG4cjThETde6GRD+GnDFARg1AfDwImhkZrLdJTOT5iunXgUyjIMQXFqR0YaMMT1Otdm+Jg/wPAJUxDDL33EBrSzN0+q5uWQ56emArgTwOwLkXwagAYavBsJn831padKu0teX9T/B9mJWAwfnGa/tICDsZTJXrXEgxMGD0jhj9mw+uCsqgHXvAzpj+n/YF4BXdz5sFYUPyLAwsr8HDwjIw4YRdFJSAFdHINtYI64YCvTpT2BPSmKKMyyMGQGA4Lt8ufEehRJ4dDog31iHt+1IO06A7O36dVOPaHd3KrUBeb0FSGu1KnGjkRGXl7MemZkp35eby57fwkIJIg8eEODi43ncLecBSX8BLrwJeD/H+69pBthbAfkF/FmIs86cYUp69WqezxtvSH/q/ft5f4Rhyc6dVD5PWgysdQCqzwOulwA3K96nHTuYrXBz4/lPmcKacHIy2evs2QTSyEiez/bt3EdVFRcEADMAM2YQ+C9d4udHjmRtW4RGw220aEE2n5xMVfX48bxftUVAABm3GD5y5oxsdaotva2O0lIe48aNVMI3by7/njaN52ZjwwWeJX5y8VhArNFo/g5gNKhPjQcwV1GU/Po/BdYMz7zD9GDaKdPfOfqrZvQONhXm/FCRF8+hCgm7a/YX23sCLUcAPd8CPNr98MciIuMiU88xq6WbmEuwVF07eNf7cbYTHaICWgxLAIDOS4DIX7KHu67Iu0cvaAHcVnZcfHR+BVi6mg/vbdsIIuJhEdYa8LoOXPsnkFHNB36fP3HcoXrxJMbPHTrE0oPjNUC7B6jQc7DHs6tqT+/fuMGHsF4PeBYAWAvkP+Q1Gbud+gDA1K4yLIwPTgEmlz7i8AgAKH+O10KtTD1+nMem1ZKJNG/O4928Eij7lL23XV5nj/O2bQSsgACmXnNyCOIAVdOCuQNAmwwgLhnQtwB0EWTAW4yLm6gonptez9RsejofyK1aSbYbFgbcX8Z/+w+Wk5iEUMvHh8AO8J7o9fxbqKjF+atrxIZyiuHKtHJRKVLZOTl84N+5QxGX2gYToHhswADgzvNAzgbAPwjI8gRSMgB3JyAfZMWjRhGIz50jCLZty0XCyZOspYr2rtu36ZoVH0+WevGi0QxlAHBcA1QMBqw9gS4teGwnT3KhtWiRnOi0Zg2v18aNTOlaW3MhYG3Na33oEJnxwIG83zodj8/Tk/dt717ez2HDTHUdzZtzP/v2caGwaRPZ9dCh8nqpQwgURavT/fsE0U6d6JhWV6uTqyvw5ptc/IhFbWIiv4+5udzXnj1Mowd+zwZDlnji8biM+DsA/6UoSrVGo3kfwH8BeLPBTz28xVQnwDaelsOlyMr9MeZ6NiVybhJ8Ew/UnOTk4AO0HsuhCi5BtX/+h4jKYtagr31OH1sRoRMIwEGDG1Z+66vIYC98IKdJ2bpS/dx5Sf1WmQWJwJk/ATdX82etFe01u/1Kpr1Hj+bDxMuLKTlF4ZjEY3PlEI8O84C+fzbt8QX4oNy9m4xVkwt4HwXKbpIFd14CPPPXmq1VVVVkNJcvA1CA4CQgew1/1/p5YPgaMme1pzRAgBs8WDLd0/8DnH2HvysbB3RfZDq95uxZowkI+CAPMPp5H9wLZLwH6IqAgMHAwA94LDdu8PwnGduoduzgfnr1okp6504y6bZ+wB3VDOOhA1n/TUggM4uIINMC+FnRvtS1Kx/8ANC+HXDAyIjbjAGuH5aqboCsP9f4HRZpaCcnLpgAArEuCcAaIF4L6L0Aewe6WVWWANbGwQuVldxucbFU/2Zk8MGfn88Mg4uLCpStgfznAeuNgG4QkASgjY7ndf8+FyNCjHXmDBcst2/zPnXvTmDasYMg98orZLxffcX7HRLCumhSEgFpxw6mbQcPJhjfukXQnTeP+xNDJR48IPAK16727cl+169nT3NlJfcrpk317s1z3bJFgt5Es3GJNjY8tpYtmXo+d47HNWlS3SppDw+y8ytXeD7Xr/PcR4wgKNf2jNNoeH1dXEzNQvR6HldW1uNPdbLEUxmPJelVFOVbRfn/ZtmzABo3jcDaAej1Oxqyv1YCjNsNRLwKeIT9sCCccRHYNRH4lyut7uLWSxB2bAFEvAEsSgcWpwNDP//xQDjrGnBoCfCZJ6f9ZF0mO4x6F1iURvFRy6H1g3BFIXDxH8AXLYF9LxCEXVvT+nFRGtD7D3WDcGEy8N1LwBfBBGGNFoj8DT/X98+mtee2bQlStrY87i0DWW8tSqLt6AsXmbqNvkIwUhSC6XffAcuWAWkpgNt1wPFTgrBLK2DyUWDIpzVBOCuLadrLlwGrKiDkpAThZ/4OjNlGENbruS8BwmPGkLFotVTlH31DBcJTgKhXTUH46lWZGp4yhXVKgMzs2h8AXQrNScZ+DWTlSKXzhAl8aJ46xRS0uzuBIimJD2CdDnA6xVGbVR0Bp/YEoGhje1VUFAG5oIAPWGdn/mxtTfBLSOA2NGkAigF4AzrjPQwKkiIqHx+CEyDTy87OEoitrQGDCwB7oP12oHQJELkFKH0RgNZI0CIAACAASURBVDXgYXzoFxdL1iuAKD1dzthNTpYp1pQUagIUF6DD3wHHvSwxFObKFO+5c2SHAEHO0ZFMW1GoEu7cmdsuKOA1CQlhOthg4P0U19jBgSB25gzv2fjxcjjFtm3cnqMjsxhOTmTs27dLl7DQUIKiVsvj2L1b/k58pxculJ9duVJmGNTRpQvFZs2b87p8+ikXZHWFRsOF1uuvUyFdUcHjWreOpRmAGYPVq+W9qi10OmaeOnRoXL3ZEv9x8X321swDsL+uX2o0mhc1Gs1FjUZzMVvvCUT9ia1Kuh/4i5USDWwbBXziBKzvDtz9Bqg09mg6t2LKdUkusCgJGPhPwPFHWnFWldL8Y0Nv4Ksu7EXWV3C84bi9wML7QK//Bhx9699OUSrNTz5vDhz/FWu0vr0JUnNvsY5cVxtXcTpw+FVgRSDT4ABTyYtSgf5/q7ssUJoNfLeIx51ynOWEkZuAKdG0Fb1wgSwmNZXg+NlnBCttNuDzNVC9HYDChc/sG+wRV4eiEMiWLiV79DEAXuuBrCMsFUw5DnT/NR90paUU6qjruhHGyU+GataDr3wCKFqgdBYw8FWZngSYyt6xg/9+/nmpqk5MBA6+DVhfBXT2tK/U2JumlNu0IRgeNvZemxt59AoEbq8FoGV6dcgQLi7u3iXQde9uVFSD6U4xDL5TJzmovm1bINYoknPpJdPSgYEyde3uThBVs2Q1I7a2JmBqA4Hic/IaO9xn73QzYy1euGoBXDzZ2RGQhKr4wQMJxPfukW0CQKoV0OltwPYQUJxHMAV4T0QNvKqKwq0BAwiIV6/yWowcyfeeOMHFxLBhTNM+eMBr4+hI5gkw1Z+cLG1JHRzIjMX1F9OY7OzIwvftk7XzVq0o5rK25sJODdQAgf3FFynoEwvAFDPnP4ALlQULeI56PevVu3bJMkBtIc5h2jT+Oz6efeXHjjEt7uDA7aiPxxI/q2gQiDUazSGNRhNTy5+xqvf8NyjDXF/XdhRFWa4oSqSiKJFeXnU84L+vSNzP/tCPHYDN/YHEvXKcnlsbts+8WgQsTACeea9htfH3GbmxwJHXgaXewMG5VBU7NAd6/QFYmASM20WlcEOjFXNigANzgOUBVHZXlzNVO/UU+zFDx9W9jdIsthQt85OzfjsvBl5MprLZPKUsQl9J1r0iiO1P0PBazrsDhE2R7S3R0XzoPP88GUNeLuB1A2j2GVASx3sw9RQXPuaq+YoKshzBpsOKgJI/AcUPuHCbdZ1/A3xwr1jBh7a7O2t5wp2ougLYPRm4+SXHDJbOBYa/QgAVkZBAu0SANcouxlppbi6w+X8AO2Nt/fmdzC7s2kVTi8BAegXr9XygA6yBtmhB8MjMJHjlfWk8p76ATxgZjWDDffqQFd2/z9Rqhw4yFd21q1ROt28PpBkd5kJHSSAOCKipmPb0lK1L5owYAKx7A/nGc9LrAd1toLqtZL9FRRKIHz5kyhuQLU6ir1hcO5E5uHMH6PMagCigQsP9dujA+3f5Mk04AIqYbGwkSz50iEyvTx/+vHcvj3XcOP787bdciLVqxcUTwIVQaSkzETOMHuMnT8pr5+lJMLayYkZDgDTA+zPPaNZy4waV06LnGuDiZe5cXvPSUs5DjolBjbC2Zn150iTu5/Jlfg+zs2u+Vx1t2wKvvso+cUVhGWLAAKbCq6upIrfEzzIaBGJFUYYoitKhlj87AUCj0cwGMArADOVJjHICuJK88w2wqT/wkR37Qx98B1SXAdCwzan/B8DrZcC820zTirm2P0ZUVwBxG4BNzwBrwsnQqkpYGx+7A1iUAkT9L+Bcyzg2dSgK7Su/eQ74siNBBmD9eO5tipb8+9T9+bJczvj93I89xAAVygvvA0M+q3/OccI+pvOP/4rXNWw6sPABr6Xo/c7L48p+/HiqWv38gAhfwHkNUG5s1en+W2Dm1dqPMz2d6esbNwBbLRAeC6QajzPyN8CkwzJDkJhI1iKsJxcskCBSWQxsH0Xlu8EBKJ0PjHnFVBWbksIUIcCHYa9exmtUBqz/B2C1gT8P/JhlgYsXKS4SrS06HUE1I4NgMmAAGaV48EfYshtAcQQqo5gqz8oig7O2JgMWbLh7dx6PqL26uQEJlwDrBKC5PVB1m4y+41hmGbRa6Zbl6SntKz08eAxATUYMADYRQEksRVqVxYByD6gOlaIjNSPOzZVAnJEh09OZmbzeBgPPJzTUOGnrHtDxLaBsBkFRtAudP0/wDg3lIuvCBQKvvT0zAwkJcl5vYiKBLyiItVtFYbbCYCB4h4TwXLdv5+/8/Zm6Bvg+sUjx9WXNWIC0GKghfjdvHnUOcXEUX6nZrPAJF4uFr78mYNb2aAsPZw+xYNGffcZMTn2PQVtb1omjonhNevTgd0l4k9eX6rbETzYeKzWt0WiGg+KsMYqilDb0/u81DAbg5lqmdj+2Y50yNZrpXY2O3sqDPgV+UQnMiQEif1W3UcUPFXl3geO/IfvdN4OjHe3cKQJbkABM2E9RWEO+04ZqIG4jsC4S2DqYdp42zmTRizNZz1b7NJtHeT6dsJb5Aef/ShV2+Gxg/j1g2IqaM4TVkRtH4N8+kufTPJJsduR604VDZSUfav36kSnpK4HT/wtcmg4oyUCzYGDGeeCZ92umyhWFD+xly8jE/O0B32+ApK28Z2O2MVUurtPlyzRxqKwke5w5UyqIy/OAr4cCSYdYFy2dD0x4WbJdgGCydi2/Q716SbMEvR7YvBqoWEov5g7zOa0pLU2mmydMINtMS5PCqnHjCGYHDxIcO4cDse8bj2cw0Lo9r8mJE3ytVy/uW7C4yEhTNnznDmB7BGi2F1hnTP/qvID7RmOQwEDJvtRCLQ8PCcpqRiyA1sqBc6atrwP55wHrYAB2BHaNhkDsZhxnKVqYACnYAgh2taWnY2OBiG4ANDwXX18CZVERAU+w4lOnuC/BcL/7jix5hLFf/MABHvegQTyf1FRjWUPLBZ6jIwH8lLHbokMHLoIA9o2L2mtQENXUAJm36NMGuHCaP5/X6N49CrkqKuTvhS2mYOZHjxL81exZhJsbtyUWDjt38r3q7ZlHQQGPRxw3wO/v1KkUdv3/pC1L/FzicWvE/wbgBOA7jUZzVaPRfP49HFPdYagGri4FvuoGfGQDHJjN1K6hig9pn55U0b5RybmwXZf8cMMV6gp9JXB7K7B1CLCqDft3KwvZijVqC/BSOtDvL3X7N6ujspgGHF8EA/umU8Tl0opTh15KJ4uur42popAq6GX+tJfUV3Low9xbvE71tTCV51HktKY9gd/ek5+Zca4mmxXMxc+PK/xbh4Dl4ZyYBQC6Z4H+O+m7bR5lZUw37tvHnztbA6XvALnXOZ961nWm2QFpVylMNIYOpTBLGFeUZLAUkX4W0HsCpfOAaa+QuYh4+FCCeJcuUkGrKMD+PUDmB4A2D/CNYpagokLWhfv1I4uprpYp6QEDCDrx8WQ0NjaATyLd1/S+nIk7dCjT6DExPNbevdm/qigEEltbyYQ6deJ2FBugzWKg7Uag+BeAZxRwcj5gt8O0PuzjI4HY3V0yYkdHAppOJ9txdDqg+SjA6hqQdwJo1sN4r8vlqEORps7JkUCcni6BWF0nvntX9tTeusVt+PszrXvvnmTF584xLRwczPt9+TJFW+7u3HZMDGvzrVtTmX30qGmK+vBhacwi6sWHDkkG3L8/r2N5OcFYgGBoKLMXAFt/1GzT3Z0A6u7O8sDatTw2dXTuzFS1rS1Vz19+KadYqUOn4/do2jT53mXL5D0yD62Wi4E1a2Rv9YMHzG6MGsVyiSgxWOJnEY+rmm6tKEoLRVG6GP+89H0d2P9HdTnrkl92Av5pAxxeQkBS9Bzp5t8PGLkZeL0CmHGWTO+H9HeuKwoSgRNvM+27ZzJ9tG2c6Vo17w4w6RDQdlLjxGnF6dzW0uYEw6JkwKcHMHorMO8u0GVJ7fODRVSV0JRkeQAtKatL2QI1+wYnEbm3rfuzhmrg6mfAipZcBACSwYfPrl25feIEVa1lRcCHQ4C9Q4HSe4BjW2BcNPDGAaBdBwKpOm2XkkJBVlwc4GAHdMsCEn7H4w2fDUw/C7gZFb2VlXxAnT7N+ztlivSMBuh8tjGKpid6P6B8PjDzFQqqRBQW8mFaWsoH/xiVycj588CNPwNWiUCzAOD5HRwZuXMnU8ZBQZLFHT1KRurrS3CurpaMeWAP4ILRU7viWaBLV6ZmBRvu2ZMPa+El3asXgchg4LFaWRHEYAe42gOJ6YDiDPR/HzBoWdMNDJTuWXUxYgGo6lnEWi3g0hnQGIC8o4Cr0eBCmHoABDEnJ/5tb0+QESMadTqyNTc3An1uLj8bEsL7eueOtJO8epULoGbNKLBKTZWs+ORJvn/IEP58+DCPUbDic+d4fgEBMkUsesiDgshWAS6QSkp4D8eO5SIgO5vpZCF86tCBLXeAcSTiHfl9cHEh0Hp58fjWrKkJtMIW08OD57F8ed214LZtqaoODOSCb9ky3mf1d95g4PWdPx/49a95flVVzKa8/z4XaBoNz03cN0v85OMJIFYjorIYOPMusCqMgqvjvzK6SimAlT19pZ/fC7xRDkyNBsImPxnwNVQDd3cwdftFMPuSy3O5OBixnmnj/n+XYNJQ5MYBB+cbU8jvEZBCxlCNPP0s0GZi/SKuqjLg0j+B5YHAibeAyiJ+fuYVtkCp7SVriweHga+6AodfJosPHQ/MjyeDr290Yl4eEGIN5P0B0BgFJ33eARbcAIKND9KiIuCDD8hoRc/vF18QHFt6Ai0OAHeW8r1DlwPPrpaLjcJC9ojevs0H+4IFUt0srtv6XkBBAlAdBFTOBeYskWIiQKqrCwr4+oQJ8jtz7x5w6E+AzQWC74R9bPU6f56LBHt7MiutlixMpEWFSvr0aWNK3R8o3UlhYFU7wNCS4J2XR0W0RsP6aFwcr4e/P/+o09LCFcvDDyjN40PfwQG4/SFQ4QNUtzcVajVvLluXXF3JpKys5MNfDHwAjBaXVkBVZ8CuJeBkLC0Im0txrUWdOC9P1olzciQrTk01TU+LjENsLIFPqyVDLi9nhgQguAYFcRvFxayltmvHc8nPZ+3Y3V2ma/fs4Tn0789zzMiQpYC+fcl2i4tlvdjamqld0YIkzFQAsu+hRpOYjRvJPkUIgZavL0sWq1fLrIIIYYsZHMzvz7JlxsVSLeHiIqdEAcz0bNnCaxEfD/zpT7w2ALMnrVvz2F58EfjFL6gXEF7T9aW3LfGTiqcHiMsekgV+EQL8ywk4/Xsg7zYAhcraViOASUeB10uBSd8BISMa3OQPFoXJwKk/AstbALvGMXVr5QB0fQ2Yc5OLg3bTG1eTVhQg+TiwfTTTwDFGc4WOC4A5cVTsBvSrv7+6ugK48m+qmY/9kvOeWw5nTfb5nZyDXF/kxwM7xwFfD6Ea27MjMOkIMOYbwDW4/s9WlQEuJ4D0/wJKE1lDnn0D6P176eIkamedOvEhtGKFnMHb3QsoexdIO8751C9cBDotlOeblsYHX0YGH5aLFpma6Wdepk6gNAOobgMY5gHzlpi6D1VUUJiVk8MH/9Spsm6anQ1sfQ+wMzLa0V8DXh0JNmJ4w8SJfGBXVsqU9JAhTC/m5QFHje/r11aq0CuMU55cXKRYqEcPMkl1y1JuLpmWvT0ZsVBL+7UCcowTlvyKgHu7gLLhvAaVlVI5LM5PHB/A18VD3M5OskOdcTRl5TNAy4+kt7SaEauV03XVic3bmNTpaa1WAvP169KS8fp1sk1Rjz9xgsclAPLYMR5HVBQZd0oKwdrKSqaoo6N5XzQavubkxP2L6+vkxLqw6Be+dEl+B6KiyD4VhaYh6jqs8BRvYXTuWrVK1ppFCFvMyEhmQNatk9OyzEOrZY175kx+Li6OmZ/t2/m92bNHZi7M9xEWRt/qefOk7sESP/l4skBcnAEc/SUZ3GceZIEFCfydjQsZ2bSzwGvFwPi9QOCAJ3esBj2Vw9vHsO/27DusSfr2Intbkg0M+hjwaN/I7VUDt7cAG3oCWwYACXsAa0fO0H0pnSIqjzo8bUXoK4Fry4CVwZznXJbNWvTUUxSC1VaTVUdlERD9FrCyNQel27rQAGTmFU7EaihSTgJrOwGXPuTP/f4KTD9Tk3lfuMD629ChrKPp9YBjM6CvAbj1CiczBY8CZl1lH7KI2FiCdkkJH1Bz50rmBrBHfGMU+8KrOgKaOcD8l0yBWvj3pqWRWc2YIU0RSkuBdR8D1sauu75/AVqPkXVrgMAhBgIcOsQHdEAAma2iANv/DjR7H/CPBm4YTUMqewM2vmRuBQUSEKKieBzJyWT24eGSDXfuzGMVqVP/1kBeBoAyIH8F0PItAHZ114frUkybM2JRT9frTYG4NkasVk6r68RJSfKaxMfzegYHE1jv3pXp6StXeJ6dO/Pnixf5Pn9/7ufaNbLksDAuHE6eJLMVKeqDB3mPfHxkWUCIphwcZL348GHWeQEe7+TJ/Pfu3VRiixg0iIyzuprZEXWK2c6OwBkcTIa+cqXMNIjQ6dj3/Oyz/HnvXi7W6ur/DQmhqjo4mMA7ahS/AxER1Dk8oSYTSzx98WSAuDCJtdRlvsDlf7IGClBRHDYdmHUDeDWfjMyvnqEEP0YUpwNn/wx80YrK4YTdrPN2Xsw2nOln6P1cX81WHVUlZK8rQ4E9Uzjm0SkQGPgJAbjvu3X38YowVNODelUb4NBLNPHw7wdMPsZadH0tTADdpmJWAytaAReM6t6IN4AFiTQAaaiHuaqEvdCb+1GU5Nub7L3HmzXFcdnZZDvjx0uHoJ5dAN0G4Jqxltr3z2TudkbFrqKQMQnP6Kgo1oTVrkIJ+4DNAwB9OVAZCVjPBOa/yO2L0OvlbFk3N8lQxO82rQGqlgGaCn7verwl2XtBAftXBYNLTGSqWqslG9NqmUbOOAco3YG2fYAy44O7MpIpVjs7mcbu1o1gJ9hwjx5kdgKIu3SRaek2bQAHN6AoB7DbxwVpofG81EDcGMW0Goi1WpmONxiazoiF7WdSEu9FixYEteRkU/V0q1Zk5VlZXHioW5n0epm2FaxY1HxPneJ1Dw3l9ioqpFta375cYOXkyH7bwEDJqLdulQKnsDBZf964UV4jjYYg37Ejz/nLL00dtGxsyKjbtOG2Vq6U7mUihC3mtGn8Pp87x33UlUZ2dOR3r317mTno35+LS7WS2xI/63gyQFyWDZQYHyYO3kCHuRQ0vZzLthivBmqZP3QoBo5i3DWR9dpTv+NiwTuC9csluVTUendu/DZLMoFTvwc+9yV7LbxP9jdyE7AgnhafDfU2G/S05Vzdjo5RhQ/IyCd+R7epFv0bPo7UU8D6Hvx8eS5T/nPiaK4hgLC+SDoqe6E1WmDAP4CpJ2pn73o9zTlEKwrAMXkXZgCGq4DOCZh4COj5thSBCbtK0Y8r7CrVqflbm7kogkKzDPsZwPyFch8AH/A7dpBhOjoy9ehovL6KAuzeCWR/BOhyAO9I2nJqNExp3rpFxiXqyMKaECAb8vBgGnjfPkCbCXQaCzzzLhCxBqjsDjiuAlwSCWoifdm3Lx/uwj2rWzemVYuLCag+PjItHR4OFFQA2njANhsY+HdZ11QLtRrLiM1T0+I6N4YRCwOP9HSyVT8/fjYjwzQ9LWr2t24RnEW72NWr/ExgINntzZsEOh8fZhdiYiiWUltfiuus01FhnZzMf4sU9enTUjHdpw+3V1LC75o416goMvHKSrYnCUW0RkOjGQG2X35pqlC2suKiLzycn1m5kulw82isLWZaGjMirVvLfmWdjgvTo0drsm5L/CzjyQCx1pom/wsfUND07KrGC5p+yCjNBs7/jWz1m2G0w9ToWK+dcQGYeYn1y6aYgTy8DXz7IvC5D3D2XaaDW42gv/KMC3SkaqjFSjEwjf1lB/pI598jiI/bC0w7DQQNadijuzAJ2DMN2NQXyLxEd6txe5nybygFDrAV6tBiYOsgLgACnqGJSLdf1M2gjx3jgyoigg/OTb8F1nYGihOBZuHAlPOAl2rGqrld5Zw50q5SxPUVwF7jzNaKwYDLVCpQ1XNiFYUgeeMGwWb2bNPfnz4NxH4IWN0F7LzoZmZtz7qkmKA0aZIE7oMHjaKyllJ8FB3N12xzgYjRBKcj0UBVd8DWEagu4X4UhaDk5iYZUOfO3LZapFVRIRlx27ZARj6ASiD0j0BhGa+Nuzuv56My4vqAWM2IRS9xTo6x5ck4hUot2DJvY2rWjExYrycwCyC+do3ArG5lAiQrjo7mtgcM4L6uXiULdXHhAg5gTdVgIGAPG8bXtm8nyIp6sfDpFup0jYZqaaFgVquQhYFGy5ZcDHz1lWnrkk7HRViXLtzH6tWmAi8RwhbT35/sf9kyU1vM8nLel9GjWSP/8EMy99hYnt/AgVw8WNTRP/t4MkDs1Ykm/85PwTgvIZbaM43GGyfeZJ3asyP7dV/OZb3WJ7Jp20w5CewYC6wOA26s4Ovhc4HZMQS/FgMaBk9FoSr7q65MYz+8xeMas50gHjyi4W1UlXLy0IqWwO1NVJ0P+CePI7iRgrf7Bykku/Y5Fw2DP+VCwq2eGatCXWxjA/zzA2DbTCD17wAMTIMvvAIUaoC//Y2spza7ypYtTbd54e8cigEA5SMBj0kEawEiIo4cIehZWXEQgNpS9fZt4OgHgO1pAFoqpB19TevCAwdKq8y7d3l8Oh2ZlEbDdPvJkwAqAU0Bx2NeugTkXwMcvwIG/BUImS5BR7Q4iZalnj0JrIIBd+woQTg0lACZpgOKfwN0HmXqL11ayvStvT3Bpy5GLIClqanpwkKeq7s73yMGUgA168R+fjyOrCx+TqSnb94kmLdsSSC7dYtpWScnMsSUFDJoLy/e97g4/k7MCxZCvl69+J7MTNN2r8BAAqhIW9vby7rw0aOyLizYrYsLX9u/X9Zlra2ZXvbz4/Y3bJBiN3Gtxo6VNeU1a6T/tzqcnPgdbN+e11zYYmZnAx9/TPV2t278Hr72GuvFly6xgyAxkSxaqMEt8bONp0c1/WNH2UO2+qxuR7HU7U18vf0sssxZ19ivaz6cvr4w6DkScGMf1k/jdxH4erzFQQrDVwGe4Q1vR1GAhL100to1Dsi+Dri3oyHIrKtA6PONA/G4jcCqUM4WhgJ0folZiG5vSEVzfVGez3aqb4YDxalsGxN9zA2NY4yNZe+pswHw3Azoo5kJGbWZaXAD+GAcNYrAuWyZtKtcaJZmVhQq6qN/y5/LJgA+48h0zee7njpFVqTRcJyhnx9HXp76A5CSAHz9IWBvHPIwcgMXWIpChlVYyAel6F0tK5NTgEaMIKtWFNkz3MWb97NKDxz7FLDfBPT+hJqBs2cJZB078lxu3iSIBgbymIS5RHg4gUTtLV1UxNSvrSvZlhqI1f3DgExturnVzYjrSk2Lenl5OYHJ3p7MvLKyYcGWYIh1paerqkxFWzqdzCacPcv7o2bFisI0s4MDtyUmT40axfccOsTz02q5INJqCc4JRnFnQIAUUanrxc2aUaAnvKcFoAPstX7hBX5Pk5PZp652zxI15agoqbYWrUfqELaY4ny+/prK64EDWRoRLNnBgaA8cyYnMrVuzWsbF2cRbv3M4+cFxIoCpJ4G9s+iSvvYL9ki5R5GlrgkF3juS8Cvd9PGMVaV0vFrdVtg1wQ6OzkGcJuLM4F+7wGOfg1vR1FYm97Ym17JWZc5bGDEOrYEtZ3UMAACHPe4qR/duIrTgBYDubAYsrTuiUrmEb+HbD5mFY1Thq4AJn4LuLRs3OeffRYYEQLcXgjkXKaafNZ1oK2RuZw4wYdnZCTV0G5uTMmqBVUA0/KHX6aiHhqgdBrQYjTfJxidiEuXJJuaNk0y6vN/BW5tAjb3BWyMCulev2NZAGAK+c4dPrTV/cX79/OB3rq1TJHfuEHxl7MzEKChlerOtwHNNsDrTaD3HAL4mTN8v2iZUbcsAQQngOlPdVo6LEwyr9atZe8yQIWxGogLCgiy7u4ErcdRTQOyTlyfYMvRkb8rK+Pv1EDs6MhrXl3Nc2jXjgAYH89j7daN/69u3uSxhofz2DMzef62tqbWl4rCc+7cmdsUZQN3dw7pAKgDEEKpXr14/UpLTacZeXuTGYt7evcu/j8cHMhWXVx4nOZTkDQaCr/EcW3aVLsftEbDVLpQfE+ZwoXH0KFcuJkrqx0c+J2aOZMmID/GDHZLPLXx8wDiigLgyqdstdkUBcR+xdfDplHkNCeWLLGpU5hKs5n2XeZHx6/8eMCrC808FiRwm/UZYagj+RjtGb8ZBqSfo//zs6uBuXFAuxkNK5kBtlMdmMdxj2mnuI0x2zgswatT446jLBfYNxPYMZptRa2eIwvutKDxDwvFAJx5h0y6spCK5OnnZC06J4fsRNT7PDz4sEtNNRW86Ku4aLq2FFCsgNLZQPBIKlvN57LGxJjOCRaOWhUFQPxuQL8YKI8ErF0BvyhOjQIIcgK8J02SDDsujnU9GxvpwFVeLucWP/cc8DAGSI4GHqwGSucAzy3i786dI3C0a0cQSElhStbZmUCRnk5Qc3Jii8vduwSd1q25CBFmEaGhBMWHD3lcwhISqCnUUhSCHSDtLYH6U9Oil7q0lJ9Xp6drA+K0NL6vrn5ivd5UPW1jw95xgLViBwfJki9c4LGI7INgxRERptaXAMHMxoY/CwbcvTvLB4WFEqCFw5ZIRatTvqGhErw3b2Y6XYSzM7MrDg687+atRRoNlc7i+/rNN3IhpY7qan6+Rw85JKNjRy4w6lNIW0D4Zx8/XSBWFLYGHVwAfOoOHHmFZhWuIcAzfwMWZzE1GfBM0/8j5N2lcGmpN9O+FQU00Jh4iB7X7aY3LvULkKFvHQxsGcihEI5+wNBlBL8OcxrnlV1dYbS0DARuruZn+r5HT+nQcY0/v7vbgFVtgbh14t+LYQAAIABJREFUNFEZvoaCroamQqmjNIfTr4TP9OBPyeiFwE0Iqfr1kwysooIgoijy4VtdzuxC3HpAseMYw7bP0YzD2uza3r3LdCDAVGbHjvJ3tzYBVu2AtALAZRgwbjMV62feIQBt3Wo8zsGSQZeUSD/rkSPlcR45ws+EhhJQc24AZVX0tO48mKKmigoybECmKtUtS0KQBJANa7VkiABBTPTiAgRpdVpao6nb2rK83Nif7ch9NCY1rdHIhUdVVd2M2M6OGYvKSi6U1HXiZs2Yaq+s5EJKpKfj4ghM6vS0osiMwIUL3GenTgTOtDQyUp1Oth4dOsRtODrKNqW9e/maAF0xhlD0X6vrxcePm9Z1e/YkK6+uZk1YbWfp7k4wtrHh/Tl4sGa6uE8fmSrfuVPeVxHZ2cyWWFlJQxCR3j52zOIfbYk646cHxJXFnJW7LpJtOjErydDaTGSbz7w7QPffND5Fq460MwSHVW0oXAJYU551nQYaQYMbD3oZF2iNuSmKow0dvIFB/wbmJwCdXmwckAsx1+owWloaqoDwOZxr3POtxk+bKs0Cdk/huZXnAiFjuRAIn920RUr6eeCrLhR3OfrRlrOLWdotNpYPwJ49+fDdtQv45z/5AJswgQ/lFf8Gtj7Lnm3FkUDX8Tk5flAdDx7woQrwAR5pJqo78zGQE0wwmT4d8G7Plq+49VSsFhWR1QmhkKJQpVtWRrAVjC4tjfVF8WDVaIDeS4GcyQCcZOry/HmCUps2BMvCQi4uNBqyvepq2cIkVLnqtHRaGsHcx4cMVZ2Wrqzkw97KisBRm2JasNrGpKbF78X762LEgGmdWLA9cWxqVuzkRKCuqiIIBgRwW3l5fH/z5mSy5eVM8ep0khWLcYPC+rKgQLZ/detGwM/NlQsdV1eZCt65UwrU/P2ZsQC4QBPXRty7Vq24oDCvCTdvzjS1Tsc6tpgdrY7ISNlGtX8/RXsGgwTmV17h7774gjXluDief9euMvNiCUuYxU8HiLOukqV+5gF8t4j1VacWNIt4KZ0DE4KGNK7Gqg7FQLDb2JcirLvbWDON/A3wYjJryl4dG96O+ji3j+Ei4f4B9u4O+Aew4D7Q9WXAyrZx28m+QUvKXePI8Hx709Jy+Go5s7fBc1PIGFe1Ae5s4ZCKERs417ix2xDbufoZXcKKU4GgYcDMa4CvmRlLRQVTu76+fFBt2UKmtXgRQbZFC+DwLqDiEyAtGjC4ASXzgYjnpEBHHenpfNgJ0w8BpiLO7QKKUgB9CJl0xj6qv5v5AiH/knXNcaqsQUwMH552dmQ/Gg0ftEKgNWCAbO85ewuArbSyrKyUBh6CDQsg6dqVqc87dwhCgYF8QN+9y+2HhPD3gg0LcFP3DwtzCV9fXovaFNOC1TYmNS1+L96vZsTOznxvXh4/r64Tu7mRCeflcb/qNibA1HtaozFlxYBpK5No73JyomDq/n1+RqSBjx0jwGq1ko0ePSoZZ9euzFCUlMgJXgCzD0LJrB4CodORMbu7c2EgPK1FBARQ3CX2Y856AdasBes+dAj4/HMuGu7f53EMGwb88pd835kzwEcf8RrGxkoHMEtYQhX/2UBcVUqHqA292OJz7XPaPoaMAcbvo1NUz7cbdqqqddtlZNarwwh2aaf4AH/m78ZhDn8DnAIav72cGDLOr7qS6dk4A/3eJ5h3+0XNGb11RWkOcGgJ691JR3huI9YD0041bGmpjuJ0YNd4YO80ptbbTALm3wXaTWuiUK2Evc2HX+bPvf/Ia+/gWfO9168zPVdeTgb52mtApwBgtS9T/Cf3AVYrgIq7gGNroHoREDGY6WHzY8rJoRlDdTXZkkhnikhLA468D1R1AoZ2Ay4s5EjK53cBrX8NHDvL902eLNOzRUWyzjxmjOwjvnyZaVd3d4IuQIC8fZtAJhYAly7JaUQBAWSFAojNRVoCnNRqaUDWh1u35rYyMsiAfXxMjTwA1o6BhhlxXalp8XvxfjUj1mhk25d6+EN6On+nZsUBAUzppqfz/pqnp4XF5Y0bXIy1aUM2m5nJ62hlJa+hYKGBgabWlwAZcffuxpGVxlYkjYb3ysaG2xfXU7zu5sZ9CKMQQPpGizS0YNgigoNNxV2ilKCO9u0pCAQoMpw2jXXkw4d5XFZWzKbMm0dBlqLw2ouFmiUsoYr/TCDOuQkceQ34zIsOUennCEi9/0hge34nRUaNETiZR1kuZ/gu9yezzrtLodNza4GF94Huv25aS9PD2+xR/rIj2bSVAxD1J2BRCtDjt6zFNib0VRxLuCKI4iVogF5/AObfY0260UIqBbi5lm1N93bQVnT018DoLfXPNq4tcm+R2d/aQFHa+P1An/+p+7p37coJM1OnksVotXQb67iQblmXpgLVKUwdzzoH9B9N0Y25QX5+PkG4vJzTfsyBurAQWL+Wc3d9HICr84FWwzlQwjlc9gsPGSLrnYrCNHllJbcpgLGkRE7yGTlSTjYSrwkry6oqCRiCDcfE8BhbtWLas7CQrFGn4/arqmQ7jFD7pqayBt6ihWx7CQzktVIbeej1BGKtluxV3bpkMBDArKy4r8amptWMGKhdsCWOQV0n1molK46P53ZatOC1TEggwIeGSlao1ZpOZQKYtndw4P0WKW+xuDp9WgrRBg0ikN65I1P6Tk6SLe/eLWu/dnaSuZ44YaqW9vDg9xBgyti8LaldO2ZhACqz4+JMf28wEPhDQvgdsLbmgqOkpGa/sbc3U+W/+hUXB5awhFn85wBxdTnrepv60WHqyr84JrDVc8DYHQTgPv/TNJaqjvwE4PCrFGCd/gNQnse+2QkH6SndfmbjZgn///bigf2zyahvb+Jne/2B/cS9ftd4NTUAJB4gkB99g+fcdioXBVH/23ggB5im3T4KODCbTLbdDNbM20xo/DZE3N4KfNUZyI0lE599g2BXX1hZmQ5tyLzCuc39/gL4vws4dQdcglnLt3Pjw7Kigg9rIXQpLqb7VlERH+7C91lEZSW9f8uvA9oSwNWKABz5KwBa1oVLSvhZwW4Bsh7hECXqjgAf0pWVTLeKQQexsQRMV1dZk75yhdsNCuIfRWGdEZBs+Pp1/i2UtHfvEpxateJ+1W1LOp1pfRgwFWqJ1KyXFxch6tYl0c4jpvc0JjVdVmbKiAFTIHZyYoaguJh/zOvEoUZnPMHo1eppoGZ6OiKC5xgXx4WVtbW8H4IVe3ry+qqtL+3tpfp53z5pwtGxI8GzrMw03ezrywUUQLWzAHSAzFcA+Nat8vqK6NLFVGktFNvV1VwIxMRQ4Ke+voMGSVZsHtbWNc1nLGEJ/CcA8cM7wLFfA0ubMwWaehKw92TKeUEi06CtxzZOXVxbpJ8Hdk8GVoZwhJ1iIEDNvMJxiy2HNS1VW/iASu2VrYHYtbTI7PEWsCiNwGnn2vA2RDy8DWwbCWx7jv3O3hHAlBPAqI1NcyVTFOD6F2TBifvIfJ/fRTWzvUfDn1eHvgo4+gtgz2SWATov4TE5BzVtOwBw8r+Anr8DqrTA1XvA6OW8jwd+z7FxR4+SScTHsw6XkMCa8MOHBILJk03FW8KYIz0d8OgFjN1D1bfofT5xgttycjKtC+fnyxrw2LESwJKSCNA6nTSL0Oulo9PgwVxc6PXSWlEMiXjwgKlXV1emYhXFtHcYMPWWBkzT0mIbANmnXi/ZqJeXaX0YqNvMA2h8atrBQYK6wVC/YKt5cwJLRoZMxwOy5i2AOC6O+2rThvtKSpJKbNGbLUw2unfn6/fuSX/n/v2l0lwAZadOvP+FhRK0NRqCqhg7qO71jYxklqO8nPVitaVkZCQXSno9PanNlc29eskZyevX89jWrSNwT5vGa/HxxxSalZVxMaDRyHtrCUs0Ip5OINZX0lt562CaZFz6kP2ogUMoulqURhFWY80lzEMx0LBic38KjO5spetTt1/SeWrEuoZn+JpHUQprtytaUqkNAN1+BbyURkOPpgBeeT7NRlaHETjtPIBhK4EXLgABfRv+vDoK7gNfDwO+W8isQvhcekSHjG7adgCgKJUuZJc/ouhtxDpalTZWYKaOB4fpmd1pIUGsXTvgxkEgrxxI3EPBy6JFZGFVVWSpGzYQ3Hx9+RA0b2M6coQPYQcHYMZsoLUqZZ2YKFnV5MkSbMW0JdFqI/qP9XoyK4ApUsHkL10iG/Xz48MdIEgUFbFWKqwx1QYeWi3TzLm5rFkGBfGcRLozLMyogFcJtaqrJdv092dNXFGYIrayqgnEdZl5iHMBGgZijUbOOC4pqQnEasGWVivT08nJvD7Nm3M76encTkAA2XliIo9Z1IpFzVWkpy9eJLO1sWGLECABVm19KRZAGo1kuSdPynGGzZrJ1O+ePfKaCN9pd3ceq5jeJOLZZ3nNi4qYTRHDGUT0709A1usJws2bE8AfPOB3ae5cLuY++YQZlB49+F2razyiJSxhFk8XEOcnACf+ixOK9kyhGMnWhQrleXfIUNtMbHyPrnlUlwM3VnJ60I7RnGfr4E3R1OIsYMCHTfe/LsngSMDlLYy1WwBdX+ViYcAHTau7GvScL/xFK9pvAkD339IcpOO8pim+FQOVzKvaAEmHAEd/YMIB2mw2hpWX5gCn/5eCOIDAubYjkHaaAzpmXWPm4FFCMdDTO+rPTBVe/gK4vQi49SHQ4xfAK7F8MGo0rA/26UOG9eabfOB36lTTVev6dclKp0+XgAKQ5Yh+4WHDWL8UceECgcLJSbJegCwtK4sPXQEYFRUSzMVEKDUbfsbYk56fT5DV6WqmZLt25XuEAUbLllxspKezRuzlxWNPTyfw+vtLIRQgwbApjLixqmnxebE9sW1ho6lmxIBpnRioqZ5We0+LcwcIxGKIQ0gIQVi0dPXowQXW7duSAZtbXwKsu4pU9r59MhXcrh3T1JWVrBeL121tZb341CnZdyyuy8SJPJ7UVC7MzA09unblYmLePKare/fmPS0vZwp97FjgpZd4rQ8e5P2pTeRlCUvUEk8eiA3VbA/6ZjjTw+f/CpQ/pNHGiA3AS0aF8uNMZyrPA879hWD57QIOT/AIp2HFi8kUTTUlZQzQVev4bzhX+confK3zS+zhHfRJ09p/ADprrYvgfOGKfNnL+8z7gK1zgx83ifx4YMsgKpkNVUCnRXQPa/lsw58VceRV4PoyiuHOvcdWqfI8LoRmXAQ8H2NU5Z2vWaMuSQe2dgNcbwODPgBeewD0U/lgZ2dT/Sx6ea2t2ecZHU3gFQ/L5GTWfgH2IgeodAIGA2uDpaVUt/ZWTXt6+FA6ZY0bJ0GpsFCyr5EjJYs8dYrpx9BQyXxjYgi8vr6yTipSrRER3GZlpawPC1ZYn1oaqL8+DJgCsV7PxYaVFQHnURkxYFontrfn74uLZW+z+ljq6ydWn5tIT/v48E9RkQTUXr34t2hlsrOT90gscGqzvgTIVJ2cuJASRjAAsyfNmnFBoHbA8vEhMwZq1otFn7mdHbel7iHOz+cEphEjpLGKqyvP9/Jl+T4XF5ZSXnmFvdEi62IJSzQQTw6IC5NoxL8sgO1B9w9SeBTxOkFjynG20jxK2lNEwX2y1aXewMn/5uD2FgNZV559g4YVTRFgARwWceJt2lpe/ACAAnSYx3r1kKVNc6ECgIJEtjVtGcjhDh7hFCs9v6P+6Ua1hUEPXPqILDjlOOu2kw4DQz9vGpjf+RrIugLMuck5zCff5usD/snBE01dGJgf48n/Zv079SQwZiuw5AbQbUbNWvzp06wbihR0cjLZiqMjlaxbt5K1CkOP/v1NXbUAPlATE/mQFNOTADmv2GDgPoKD5WcOHiRwdO0qWV9RkVRFCzWvwSAf2IINV1ZKO0Mh0hJtPCEhPI7qaqnSFa0+9dWHgZqMWLBUDw9Z13RxkVacQO01YnH+Iv1aHyPWaMj2AC5a3NzIzh8+5Pv9/fm7pCSeU2AgFwMpKVz4uBqHVpSXy/5Z8wxB69ZMGefkmIKzlRWZtEg7R0TwXNXWlzY2Uli3f788B3t7qXjet8/UNjUigt+Rigp+f9T1Yjc32ZJ09Cj3c/Ysa8CuruxpvnxZXs8+ffh78zGGzZpRtBXWiPGilrAEnhQQ599jG87ZP9HP2Lc3MPxLYHE2MPAjjpV7nMi8xJahL1qRrRqqqTR+4SIw+QiV1k21tawokL7S59/jNtvPJGt9dmXT69WVxQSkL4LZ1mTjRDvIWVdpPNLUyL0FbH4GOPYLpn67vspRh4GDmrad0iyy4eFrqFyedor+2X3/TO/sx/XF1ero8zz3FjDm65qmHyKKighg3bvzIb15M4U23bqRHfn7kyktXUqWGh4uRTUiEhL48ASYllQPkzh7lgDi5ibtEwEC4s2b3La6N1nU/Lp2ZboaIKvNzWWaVDx0r18nGLduLUHMXKQVH08gDAqSNd2kJAKlUFwLIG7Rgj+rgbiiguBrZ8dzUteHgfpT0wD3oyiSgao/U59yWqORjDwzkwukgABuJy2N2xULCQGq5uppsVC6eZP3TaOpOavYwUG+JlhxbdaXAK97aCiBX90rHBoqnczUqWZRL/bw4IJBZD5EBAVJEP/6a6aXu3enJmDyZKbQP/+cqW0fH25HzcYtYYlHiCcDxBUFdKfqvIS1xumngfBZjTe1qC0UBUjcz5Tsuki2DGmtyLAXJFJp3Lxb07dbWQSc/TOwzJ+mE/oKoO0Usvbn1jadtSoG4OaXBOBzf+FrXV+js1aXJU1XfxuqgfN/A9a0Y/3WNQSYEs30uPB3bvSxKRSctZ8F+PWSrw/+FLj4D/ZUfx/Rbjrg3qb+95w/T5Z65AhHyvn7M+XXpQsfjpGRFOa8+CIf0uHhpouEoiJZFx4+XLI3gCxL9AE//7wcIFFdLd2Zhg2TRh/Z2WRCGo1MkSqKZMP9+vF3tU1ZyssjG7SxkWCt9pYGJGiFhJAJZmcTbD09pYNVZSWZo62tNPLw9OR+1fVhoP7UNCCHPdQGxPX1EgONrxPX1sZkMBBkxWtC2dylC0H9zh25n969uXC4fl2eb1gYFyZq60uNhulgjYbXXhwXwJq/szMzIuL9AO/F5Mn8zJkzNXuIRd1++HBg/nxmO2JjWUOeM4dq+e++Yy97y5bM3FjGGFriMeLJALFzELAkh4rbxk4Fqiv0lUDMGvbZbhsBJB9le1Pfv7C+PPCjR1NXV5VwEP3yFsCp3/Hn1uPoKz1q06Ox9rQzdAE7MAcoy6YV5JybwKCPGzf5qbLI9D98TgxtN0+8yZ+7/YrHF9Cv6ccGUKmeGysnE+XHA2ffZV3dxonX+seIyko+OG/f5gP6lVeonLW2JlNLTubDXDC02bOZZo6O5sNe1IVFO0lPFes2GNjiBPBhL+qcAGvADx8StEVrDSBZU1SUBKpbt5gW9/CQ7UcJCQRRDw8JSEKw07kzj19M6AHqTkub14fVRh5A/YppQHou15aaVv9tPpNYvY3aGDHQ+DqxmCjl5sbjLiurOz1ta8tMByDr646OUiQnWLFGI7MXwvoS4AJFtI2pe4htbaUv9IED8hwAZjWEwnrbNtmXff8+syw9evB7Y23NY2nVigsojYZag8WLqV24eJHZAbGYsoQlHiEesfn2McPes+lszTzK8ykmuvQPplMBzhWO/DXQ7oVHry1Xl9Mq8+y7HIAAAMGjCE7NI+r/bF1RlMKhDHHGWbiurVlvDa7FurGuSNhHM44R62hHeeF9ulIBPO9nV5uy2KZGSQZw9DXg2VXA9RV0y8qP5/zgYV80fUbz44ROR+AND5e+ziKuXuXrom6cmyvTz3v2MO3r7c0Hqqsr1azq4z55kmlUT0/W8UQ8fCi3o3bqun+/ppWlORsWKV/1lCXBkNWTlgA+sKuqyCSdnWu2LQE168Pm1pYCUNyNi7emMuLaZhILUBNALLYp9lEXIxYK9AcPeC6urry2OTkEKB8f3q/0dLLK4GAyf6EUz8yUyvSzZ9keNmgQQVTUYK9cIdC6ukrry1u3eC8FMPfty7RxaiqzFwLYW7Xits+f52Jt7lx5v7p04f29do1p6MBALsa0Wm7Dx0e2s3XtynsuFmhaLf/doQPBWJQhLGGJR4gnr5puahQmscd2qTfBrTQLCOgPPL+b7LLj/EcD4eoKtvusaMk6a3kuVcbTzwLjdj8aCFeV0S5zRRBB2MoO6P8hjzNkVOOBLT8eODiX6eajb9BWUoBwz7dpPvI4IAwwJV2RD+ybAWScB3obXcAG/xvw7/PjzkwVQGwOworCB6So/R07BqxcSQDr2pWpyNBQmWqcPNm0zSkjQ/aQjhsnwVztXdyjB+uB4nUxMUdYWQJksOnpBAZR88zNZWrV2lqCbmIi06je3nKb5mrprCyCnru7BD316EOg6Yy4oRqx+UxirZafMZ9JrN6H6GMW6fDMTN4DBwembCsq5IzfutqYRHpaq5XXSLBid3eCXnW1XLw4O0vnMrVHc23Wl1ZWsrf4229NRxwOGcLvUnIyU9EiRD+ypyePvbCQvtCenjQHOXCA2oSCAp5TYaEcvCFC9D6r2+UsYYkmxn8OEGddpbPWiiD22BqqyAynnwOmHDMC2yOcjr6KDHBlCNt9SjOprJ5ygn23dYmJ6gtFYZp3VSjtMhUDRxsufABE/rJpSu2qEmDnONpjdn0FGPIZkH0V8OxI8VnfPzd+3GF9ETySgrlFqcCIryhoe9R+7R8qEhMJLuXlTB9mZtL0o3dvstbwcAL4okV8sF+4IO0eq6tlSvqZZ0xrxrduETQcHExZcm1WlooiB8736yfZpUipdutGNgeYirREz7EA4rrS0gUF/OPkxP0C9bcuAQ0z4vpS04Bss6ms5ELC3p7XTZhsCNvM0lJ+VhyHAN6G2pjc3ckuS0sl2xdAfO2aPA7zViZAZiEuXJCLA7X1pdqco3Vrgn5FhakIy8ZGpqi/+04et6Jw/6WlHPIwaRK3IWYzL1lCtr5sGZl5p06m7VCWsMT3FE83ECsKcP9bYOtQTi2KW0+w7fIKMD+egwp8ezzatg3VFE2tagN89yLH9/lFAZOOUFndVAcrEZmX6di1Zwq3GdCfjHXosqYPVVAU4NsX6fLVZQlfazMR8O8LdJj7aOKzuqLjfCBsatO8q3/suHyZD+NduyimmjJFDpXX6aSa2dGRBg3R0cB77zFdffy4TIOKeiJAsBECreHDTVmkeJgPGSIFTomJVNs6Ocme4IoKplQBWdcsL5dqWtEHnZDA/QUESAZVV9tSUJAUYhUXc3/NmvE7oW5dAhrPiOsC4roEW3XViesSbKmPXavlz2Kb5uppT0+mtcvKpLlGq1Zk1w8fSjbt6ipryuopSQMG8DyuXTP1iB4+nK9fuSIXBuIYhWvXjh3cx9q1VED36SOvv0bDY715k/d8wAAKtu7d4zavXTOdYWwJS3wP8XQCsb4SiP2KQ+a/eZbOUHbunFq0OAsY/C/ANbjh7dQWBj0Qt4FzaQ/M4Sxfnx4c7jD1BBA48NG2W5JJj+l13YDUE5yFPHorMPlo0+0yRVz5F8VTQz6XqeHKIiB0Ant7y3Lr//xPKRSF6caICDKVtm3l72JjpXhLKJfXreODvl07OiwJwc+4cab+1MePE+xatjTtQb54UVpZCjEWIGvDfftKcL56lQ/ntm1lejkmhscSFibHKZp7Swv7R4D7B2qmpc3ZcGkpP+fkRKanKDI9K/bTlNS0+n3mgq26lNPmgi21clpRyKqF97Q4P/WMYrFfc9FWba1MADMPALMOIuXs6ChfV7NfZ2eqmgH6h6ttJgcNItCnpTGj4unJRdGlS8yWqBcNaq9oDw+mrIcP537Np4FZwhKPGU8XEFcUAhc+YJ12/ywaXLiFkk2KqUVNHVIgQjHQqGJtJ9ZB8+4C3l1ZW55+tvHDHcpyCeAPjav46gqqq1cE0WNaowOi3qWfc5uJj15bTYkGzv2ZYJ4TQ/HYpmdo/5mwG+jzDhcnP5fQaOiqNWSIbDcC+OAXQFxQwKEQN26Qxeh0TEMvWULHLXt7WesEmKIUtUe1QKuiQgq3hJUlQIZ3/z6ZqRDt1NayBNTsHa4tLS1UxCEh8pzqqg/XZW1ZXs5tOzrKBUZTU9OPy4hdXPiZwkK5KDBPT3t4MBtRUsJaLUBw1unIiIUpSadOTO3Hx0szD3d3vm4wmLLi3r1rWl8CvA/e3syAqAH94UPuLzKSs7BHjOCxT57M6790KbcjPLLF/gF+Bzp25HfJXLtgCUs8ZjwdQFyUAhz/LfB5cyD6N7Q+9IvieMO5t1hffdQ6qKIA93YCX0UAuyeRYXp2AMZsA1641DTRVFUZsGMMFwiHXwbu7SKzjv4t+4vbz2QduNd/P15PdHEaJ0JZ2XMoxcF5tP3s+TawOJNuWd1/8+MKqJ6GqO18xaD6rCxg+XKmN+fN4wO3vJwAZmPDh+jEicBnnwH/+hcBWUxc6tuXTElEbVaWgGTDUVFS6HX3Lh/wXl7yvdnZrC07OEjby8REPtz9/WXt1zwtXVbG87CxIZAAja8PCxZrMMhar2C+TU1NN8SIRQkgPZ3702gabmMCanpP29rKwRnCa9rGRtbja2PFZ88yKyA+X5v1pU4nxxsePiz7xn/5S96jkSN5jhoNF0HJyXxt9GimrQ8e5H0Tx6mOn9v/OUv8KPFkgTj7Omf2Lm8BXPw7W4dCxwPTTgPTTnK84aMIsABp8LG+B7DzeSD7GuDWFhi5iSYioeOa9p/KoAf2TgOcW5JBl+UAO8cCBQkUdE0/S4MPJ/8GN9VgaG0427f3/7AveE4MMOAffO1pruE+iYiNJRM7dQp44QXZThQfz4esuMdZWVRG29kR5FauJMN1diZrFlFYKK0s1Y5bqancpp2dBArAlA2LfQk23LmzBD1ztXRtbUvq/mEBog0xYsFazYVaahexpqamGzL1sLbmwkOvl6+Z14nd3ckcCwsls1TXiQVoiozB1avyte7d+ffly7KtysvqThdOAAAaPUlEQVSLn9frTQFabX2pHn0YGMhtV1eT6ZaWkv1evmzqhBUSYjoHevFisvZr1yyjDC3xo8WT6SOuLOKQh/sH5WudFwPdfvF4wx0A/mdOOsL2nnRjq4JLMPuAw6bRYvFRtnnkVaCqmAIxnQ0XC584AIM/AzovevQFQ23h4EmLSUs0HFotBVKDBsmaLcCHq6gjX7tGljN0KFOgo0fzc7GxVN1ev86HtpUVU9LCytJbJa4TSumoKJlGzs7mfmxtpSBLr5ftN6IGqk5LCzDKzaUHsouL7EE1T0uXl7NObWsrWXRDjLg2IG5satq8l1iAvEjFirS+RsOFQXY2GbuXV02HLY2GwHbhApm/tzff5+3NRVFyMj/TsiXPTWQRAgL4c7t2ND65ckWKrITD1enTTEvb2Unry82byX7bt+d9vH+fqekOHSjsc3bmfrt25T1OSmK7W3AwNQR6Pbdlb88yRkwM9y1et4QlfsB4Mow47w5B2NaFrG9xFttyHheEU6I5L/frIQRhpxac4zvvNtD+hUcDYYDe0mmnmc4WrUfW9hwakR///YKwJZoWgwbxQasGYYOBqeCgID5ko6PpvhUQwAdts2b8u1s3uiv99a/8c/YsGZNWK1OeANnWnTsEYMHWAMnMIiMlON+7R/bl7y+BXKiH/fwkqKnT0oJJ1yfUEu9pausS8OiqabFtnY4M12CQNWDzOrG3NxcM2dkydWxeJwZqqqfFiEHAtDVILdoSCwkfHy6uqqpkuxhgan156BCwaRNrud7eBFVxPi1aMG2/cCFZ76pVLBd4eMi6tYgOHSjQsoCwJX6EeDIIorMhk1yUBvT5I+Dg1fBnROTcBArN/tOknWGL0+b+BONmPpyENP8e5/g21b9ZHTFr2Gc8fh/r1BkXgatLgQNzOT3owcEGN2GJHzlSUwmmmzcTXF58kXXN5GTTWcSpqQRqb2/WCGNjCSbt20tWCEjFtWBhANmjAA41OJuLtICa3tKABCdRQ66qkmAgepzNjTzUrUsC0BtqXRLbBiSYN1Y1LbYN1K2cFseorhOL8xA1c9G2pb4GN2/KVLRoA7t+XR5rUBD3UVDAHnERooxw+rTcpkYj70FSEj8bFUU1tNpjukULHpudHXuGO3UCvviCnxfpaUtY4gnEkwFiz45Al8WAdRPndaZE01t513j+J864SH/pjX3Y4mTvCQz8hEMeOr/U9BGH5pF4gD7LbqHc579d6XCVeRHw7QWM2gq8cLnh7Vjix42EBIJKly4UaAmDjZQUOas4NhZYv57MNyiI7503jzNpMzOB3/+e6cmsLL7XykoaTgAybdm+vUwbl5TQHESjkSIkg6FmWrqqSj74BVilpvJvMUoQqCnUKijg9tzdJVNriBGLKUtqZtcQI3Zw4DkUFkqwrk85LQDVvE5sYyPHSwqFuJcXU/FFRbwfAK9fcDCvi/DhrquVyd+fTLu8nCCbkwN8+CEXVMOHc9HVuzev9ZAhfM++fTyPgADuU6TXe/UCpk41nY9sCUs8gXgyNeJHiZSTwK6JwJhvgOg3OTwhw5iesnUFev2e4NtUcK8vSrMoHvPpQeMQ74jH98i2xA8fkZFkmsJWUkRyMplTdDTZ0syZZLbe3pItBgWRKe3ZQ8AQfau9esm6q8FQe8vS9ev8OzxcvvfBA+7D11f2GAtf5pYt5SLBPC0NNCzUAhpmxAIk1an7hoBYo2HtOj+f5+/kVBOI7e0JoPn5XCAIH2j1uQAEzYQEZgDatOG2w8NZc4+NlRmKLl34vqtXZb29Y0eqne/f56JEXIdnnuH2jhwhM46J4cJH+EsDvKdFRWxj27qVM6snGtsJ8/NlRqFFCzqxiZS7JSzxBOI/o7iZepqMdMR6zup9bi3w8BZg7Qj0fQ94MZnWkd8nCAMczTh6C9D910DAMxYQ/k+JZs1qgrAQPp0+Tda6YAHBMStL1nIVhYKfM2eovn79dbLkiAiC7PbtBNXbt/ng9vGR4KMe8CBqnkBNNgzUbFsCagJxVRWPTauVYq7agLixAx+0qv/qDaWm1durSzkN1DT28PMj0KWkyBSzue80ULt6ul07MuiEBAIlwMWDSDmLWnF0NIV37u68N2+8wTqwwcAecnEOQhRmZwfMmEHgXbmSiwrBxEXU9n2xhCV+xHj6gTjtLNuPRnwFtDS2k3iGA359gL7vAj3fsgCkJRqOlBS2suj1nMAjGGRWFuvHBgP7iuPj2YMqBFK+vhR0hYcD//4306D79/Oz6pYlMUnI2Vmmm2tLSwM125YMhpoTl4Qfsq+vBE5zINbrqQK3spLMuiF7S/W/62LEQMPjEMWxiXMHeBzi+AXYeXnxmuTlyc96e3N7BQUyJW9tLZmwWNAAslXs6lXg4495D1JSOBrT35+f8/Ago/b1Bdas4TVp3lxeQ62WGoDu3Xms5sIsS1jiCcfTDcTp59mr+9yXnIQEcAhC5hW6Yp17j57RlrBEQ9G8OQF20iRpxgHImcLbthEoZs+mCEjUfQE+uKOjWXN84w22vfj4ULm7axeVt2qRlgDOpCSmdps3l0AmAMnRURpjZGaSQTZvLkHRvD4M1ARi4Ubl4iIXBA25aqn/XR8QmzNiZ2eeV16e9Fo2Z8RA3W1MgMwECD9nwLRXV91TbDBQxb5jBxcZo0eznjt/Pg1U1A5brq4E9eHDqaBevZqfr642ncLUowfZsajfW8IST0k8vTXijIvAN8M4NOH+t8Dlj5mOLs3kPF/3dkCPtx5PEW2Jn084OZkacQBMi2ZlMR3t6MiHtJUVwUYAcUoK22H695cAGh7OVOrq1XTqunlTgpNgdUBNb2nAVC1dV9sSULM+DDQ8/hCQvcCPm5o2Z8QaDdltZiavj5dXTUasPgd1nTg0lG1h9+7Jmnp4ONXosbHSRtTfn+eWmwt88AFrv46OwD/+IY8xLY1OaFeu8DNRUbxXeXn8ecAA1q9XrWKqOzubqWcR6nKAJSzxlMTTi2IZFwD39lRCO/oBgYMB9zDApdWj9wNbwhLqyM8n+/X0ZPpZAFR+PoVUqanAxo3A2LFknwLkAAL4zZv83axZZGmHDgGffEIQmzix6fVh0f4D1GTEej3BRqutna2KeJTUtJWVtAQVimLzfQAEycxMaenp5ESFdWEhe4cdHKT46sEDOXtYpOrj47lgsbIi+3d357Zu3qQr1o0b3O60aazp3r/PEYTXrkkAd3DgMc6ezTS0VsvFj6grA3yvvT3ZdGamHKhhCUs8pfH0AnGXxfxjCUv8UOHiQuV0cLCp3Wl+PkF3wwYCdJs2tL0Uc3vz8tj61KcP09zNmvHP3LnA3/5GJufiQsCwsSEYODjw3wKIRVuPotSsDxsMpkYZYp8AgUoca22M+FFS0wCPr6iIaXY7u8b1Eosaenw8jzckhJ/18eFCIiODIig7Oy4yHjzgn1ataLji4MDj/e47XvPEROCdd6TCOzeX1/jUKZmJcHAg6Ds7m4JxdTWPXdTKO3UimAuhmyUs8RTH0wvElrDEDx1arRzXp478fODoUWD8eGmTWVpKsC0p4YhFMYRAGGwA7IFNTqaKd8wYguDFi0xfp6WxhqnXkw0KwMjLI9t2dZUsNCeH7/P2lvXsxiimgaYxYvWIQDs7bq+8nP+uixGrjwUg6KqBGOCCIiODTF+okQMDCcL79vE6JSVxCMOUKQT9Bw+Av/yFvx89miBvbc3rNH06FdEODgRk4dzl4iLBWK/nfRN1d8DUvMUSlniK4+kWa1nCEj92KApBaNw4Oa4Q4MPfyoosuX17Cn+qqiR7y8ykqcTgwbKHWKula1RlJbc3cCBT1gYDbRbfeYf1acC0PizS0vXVh4HGMeL6asRqRvwo7lqATJ3XJti6fp0tQzNnUtg2dCivwcsv8/dt2pgee0QEa/LCvtLKitfYx4fX7euvZRpchKsrwVh9rSxhif+wsDBiS1hCHRoNlbn/1979BllZnncc/127W7YCy6wK2WhgAXdZQEAiLBiSjeIS/qljknea2Dg1M0xN66SZZtJEp28zmbRpmkl9YyJNMjrjqBVqOgaFVM1ECCKxQKikMZkKxD8sklIRhhX36otrnz7nyPKn7HIu3PP9vGKfPXvO9azg77mv577v572OHo2Z011dsb+1VN7vfPvtuJe8enWMIIvZzO6xMUixG1RXVxyfMyc+Y9y4CKJFi2Ly0dNPl+1XqXp0d7Yj4uI+djHiPtvW9HuDuKmpbAP390dbvfjsyi5AUePevXFPdtOmaAd3dEQbfWAgLlK+9a2yzX7wYFygPPpobKZx0UXxuubmuOd+//3xHs3N5SS46dPj+cHFWu7i/rMULeg1awS8XxHEwNkoniVctE2lCImGBunhh2MXqHnzYjOQIvy2b49JXT095b7IxfGmplgOVeyzvGJFPKC+qysmMbW2xr3Te++tnu199GhMYrr88pNHxO++GzU1N5/6WcSVfz5dEBfve/RotHxPnIg/NzbGhcYDD0gbNsSIeNasGAW//Xa0qT//+XJTk/7+CNyNG6PFbBbHpk6Nn1m/PpYlFZPELr44Rr+PPBJrf09ULE+cMyc+e8OGeI/K/bSB9zGCGDgbn/1sBEVli/fEiVjzOnVqOUpuaIhQee212ILxjjtiA48iNA8diuO9vdWzsPfsiRHyjTeWE7mWLYv7zbNnR+u1vz/W1j7+eIT+ZZdFMP7oR9HSrXz4xM9+FmtrK3fc2rEjLiiK0XVfXzwSsL+/nHW8bVsEZxHWLS3Sd78bFxjz50drubMzRuPr1sV972XL4rXuUduePWUQHzkStR45EqP+BQvKSVXLl8cyoy1bYmRd/G6nTYvfz49/XHYHCtdcE+uACWGMIgQxcDbGDPEAkYGBCKpPf7ocJZtF6D3ySLSqJ06Mtu3x4/H6detiTXJ/f9laPnYstm287rrqPY937YqAWriwbOtefnm89utfj5qOHIn1uBs2RCDecku0gp95Jja9+MxnYm3tq6/GUqB9+2LE2dsbx374wxgZ33prfP6BA9Einzq1fGqVJH3pS7Hhxk03lfW1t8d2n729cd5Hj0ZIHzgQs8OLwJ4wIToJP/hBtJiLIG5sjA1Wvve9GPVXzlxfuDDOo3JrzELlumBgFCCIgXO1cmX1khkpwmTnzgiSefPiWHNzvG7z5mhJL14co9PiXuvGjTEBbNy4GDFL5T3pa6+NiVBFEG/fHvdfjxyJY62tMXt4woQIxKamaBUfOxbLgT73ueqat26NyU2FN9+M91+9Or7u7IzPHRio3tXrkkuiJf7OOzGb+dixuGc8MBDPap45s1xffP31sV3oF74Qdba0RK09PdGK/vCHy99Za2vMMH/ooZM321i5suw0AKMYs6aBc9XQUM6QLrS2Rmt11aryWHNzjD63bJE+9akI6/HjY7T4yisxeuztLTe4kGJEO3du3DMuZiQfPBgjxJ6ecr/kgYHYterqq6sfZrBvX4zGi/XHUnxeMbms8M470WIvJpgNDJT3jovPfeutaAV3dsaFgBSj1csui/N88sn4mUOH4hw6O+N++rPPxs+OH9wLvniM5ObN1RcvM2fGDlnFxUahsZEWNOoCQQyMpBkzYsRZ+djB5uYIxBUrYvQqxSjx8OGYVb1qVQROEcTFrl1Ll0Zr+I034meeeSaetdvRUQbx7t3xnt3d5TOOX389ArCnp3y+76FDcZ96yZLYcEQq1ysvWRJhLsVuYpdeGm3q556LY/v2xZrc3t7Y2KS/P2pqa4vQvfTSWHJUBLEU5/Tii1FTMZmsoSEuRA4frg5iKSauLV8+Ev8FgPcdghg439ra4t5t5T7U48dHW/iSS8r1ykUQP/VUbBgydmy5S9Ubb0RrePHiuDe7d29MjnruuQjcjo4yiLdti2C+8sqYOCVFu3zu3Bg579gRx/bsiTb24sUx0h0YiPfo6Iiff/nluIDYuzc+s60tRvvPP1/9fOAVK+I+9f79ZRCPHx/B/ZvflCNiKWZF33Zb9bODgTo3IkFsZl82Mzcz9pMD3mvMmAi8yslIY8dGGN1wQ3n8oouiHfuHP5QzoFtayvXIPT3xXpMmxT3knTsjPDs7pcmTI9iLvZsXLIiJUQcOxOh45864EJg+Pb7u64vRcjEju6Ul7vUWQdzcHPVt2VKOiKUYpW/eHMeKIJ40Ke6H//a31eucFyyIdvTkydW/j/b26qdbAXVu2JO1zGyKpOWS9p7ptQAGmcVM4vdauDBmLBfLh8xiJPrmm+V6YrMItyeeKIO8sTFGq+vXR5AWo9AZM2KTjYaGmHFtFqH5859H4BcPmli0KI719ZU7Y11zTaxjfvfdcqvKiRPjvvWOHdX3dK+7Lu4zV+7tbFZ9rxzAkEZiRPxtSV+R5CPwXkB9W7bs5NnDH/1ohHblfef29rivXPls3Y6OaCNXrieePTtCc/78cuQ9f34c6+oqA3/OnBhNT5lSfk5LS7S329qqn+G8dGm0oyuXdI0dG0uRmFwF/L8Na0RsZjdL+r2777DKthuAkTNjxsnHliyJ1m/ljlmzZsWM6MrHKXZ2Rju68v50W1uMiotdvaQI39WrT95AY+XK6h24pGgrL1ly7ucDoIq5n34ga2abJA21o/o9ku6WtMLdD5vZf0nqdveDQ7xWZrZG0hpJam9vX/hK8eg3AABGOTPb7u7dQ37vTEF8mjedJ+mnkopHoUyW9Kqkxe7++il/UFJ3d7e/8MIL5/S5AAC835wuiM+5Ne3uuyT932yNM42IAQDAyVhHDABAohHba9rdp43UewEAUC8YEQMAkIggBgAgEUEMAEAighgAgEQEMQAAiQhiAAASEcQAACQiiAEASEQQAwCQiCAGACARQQwAQCKCGACARAQxAACJCGIAABIRxAAAJCKIAQBIRBADAJCIIAYAIBFBDABAIoIYAIBEBDEAAIkIYgAAEhHEAAAkIogBAEhEEAMAkIggBgAgEUEMAEAighgAgEQEMQAAiQhiAAASEcQAACQiiAEASEQQAwCQiCAGACARQQwAQCKCGACARAQxAACJCGIAABIRxAAAJCKIAQBIRBADAJCIIAYAIBFBDABAIoIYAIBEBDEAAIkIYgAAEhHEAAAkIogBAEhEEAMAkIggBgAgEUEMAEAighgAgEQEMQAAiYYdxGZ2l5n92sx2m9k3R6IoAADqRdNwftjMrpf0SUlXuftxM/vAyJQFAEB9GO6I+E5J33D345Lk7geGXxIAAPVjuEHcJenjZrbVzJ41s0UjURQAAPXijK1pM9sk6YNDfOuewZ+/WNJHJC2S9LCZXeHuPsT7rJG0RpLa29uHUzMAAKPGGYPY3T9xqu+Z2Z2SHhsM3ufNbEDSREl9Q7zPfZLuk6Tu7u6TghoAgHo03Nb0ekm9kmRmXZLGSDo43KIAAKgXw5o1LWmtpLVm9itJ/ZJuH6otDQAAhjasIHb3fkm3jVAtAADUHXbWAgAgEUEMAEAighgAgEQEMQAAiQhiAAASEcQAACQiiAEASEQQAwCQiCAGACARQQwAQCKCGACARAQxAACJCGIAABIRxAAAJCKIAQBIRBADAJCIIAYAIBFBDABAIoIYAIBEBDEAAIkIYgAAEhHEAAAkIogBAEhEEAMAkIggBgAgEUEMAEAic/faf6hZn6RXav7BpYmSDiZ+frZ6Pv96PneJ8+f86/f8s899qrtPGuobKUGczcxecPfu7Dqy1PP51/O5S5w/51+/538hnzutaQAAEhHEAAAkqtcgvi+7gGT1fP71fO4S58/5168L9tzr8h4xAAAXinodEQMAcEGo6yA2s7vM7NdmttvMvpldT62Z2ZfNzM1sYnYttWRmf2tme8xsp5mtM7PW7JpqwcxWDf59f9nMvppdT62Y2RQze9rMXhr8t/7F7JoymFmjmb1oZv+aXUutmVmrmT06+O/+JTNbkl1TpboNYjO7XtInJV3l7nMk/V1ySTVlZlMkLZe0N7uWBBslzXX3qyT9p6SvJddz3plZo6R7Ja2WdKWkW83sytyqauaEpL9y99mSPiLpz+vo3Ct9UdJL2UUk+Y6kDe4+S9J8XWC/h7oNYkl3SvqGux+XJHc/kFxPrX1b0lck1d0kAXd/yt1PDH75C0mTM+upkcWSXnb337l7v6SHFBeio567v+buvxz881uK/wl/KLeq2jKzyZJulPT97FpqzcwmSLpW0v2S5O797v7fuVVVq+cg7pL0cTPbambPmtmi7IJqxcxulvR7d9+RXcsF4A5JP8kuogY+JGlfxdf7VWdhJElmNk3S1ZK25lZSc/+guPAeyC4kwRWS+iT902Br/vtmNi67qEpN2QWcT2a2SdIHh/jWPYpzv1jRqlok6WEzu8JHyTTyM5z73ZJW1Lai2jrd+bv7vwy+5h5F2/LBWtaWxIY4Nir+rp8tMxsv6Z8l/aW7/092PbViZjdJOuDu281saXY9CZokLZB0l7tvNbPvSPqqpL/JLas0qoPY3T9xqu+Z2Z2SHhsM3ufNbECxF2lfreo7n0517mY2T9J0STvMTIq27C/NbLG7v17DEs+r0/23lyQzu13STZKWjZaLrzPYL2lKxdeTJb2aVEvNmdkfKUL4QXd/LLueGvuYpJvN7AZJfyxpgpk94O63JddVK/sl7Xf3ogvyqCKILxj13JpeL6lXksysS9IY1cFm6O6+y90/4O7T3H2a4i/pgtEUwmdiZqsk/bWkm939aHY9NbJN0gwzm25mYyTdIunx5JpqwuKK835JL7n732fXU2vu/jV3nzz47/0WSf9WRyGswf+37TOzmYOHlkn6j8SSTjKqR8RnsFbSWjP7laR+SbfXycgI0j9Kapa0cbAr8At3/7Pcks4vdz9hZn8h6UlJjZLWuvvu5LJq5WOS/kTSLjP798Fjd7v7E4k1obbukvTg4EXo7yT9aXI9VdhZCwCARPXcmgYAIB1BDABAIoIYAIBEBDEAAIkIYgAAEhHEAAAkIogBAEhEEAMAkOh/ARbffg6ShCI7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 50\n",
    "x = np.linspace(-4, 4, k)\n",
    "y_u = np.sqrt(16 - x**2)\n",
    "y_d = -np.sqrt(16 - x**2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "\n",
    "ax.scatter(0, 0, s = 100, fc = 'k', ec = 'r')\n",
    "\n",
    "for i in range(len(x)):\n",
    "    ax.arrow(0, 0, x[i], y_u[i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'r', alpha = .5, fc = 'None')\n",
    "    ax.arrow(0, 0, x[i], y_d[i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'r', alpha = .5, fc = 'None')\n",
    "\n",
    "A = np.array([[3, -2], [1, 0]])\n",
    "\n",
    "v = np.hstack((x[:, np.newaxis], y_u[:, np.newaxis]))\n",
    "Av_1 = (A@v.T)\n",
    "\n",
    "v = np.hstack((x[:, np.newaxis], y_d[:, np.newaxis]))\n",
    "Av_2 = (A@v.T)\n",
    "\n",
    "for i in range(len(x)):\n",
    "    ax.arrow(0, 0, Av_1[0, i], Av_1[1, i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'darkorange', fc = 'None')\n",
    "    ax.arrow(0, 0, Av_2[0, i], Av_2[1, i], head_width = .18, \n",
    "             head_length= .27, length_includes_head = True, \n",
    "             width = .03, ec = 'darkorange', fc = 'None')    \n",
    "n = 7\n",
    "ax.axis([-n, n, -n, n])\n",
    "plt.show()"
   ]
  }
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